Find minimum given velocity at mean position so that it complete vertical circular motion. In the previous section, we defined circular motion.

A small ball of mass 1kg moving horizontally and perpendicularly to the rod with speed v, strikes the rod at its mid point and sticks to it. 4: Circular motion. An object in uniform circular motion does experience acceleration, even though its speed is constant. Circular motion is also demonstrated by an automobile that is turning in a curve. Between X and Y, tension will balance out weight and hence the string will always be taut. It acts towards the centre of the circular path. In contrast, if the ball is attached to a non-rigid rope, then this constraint is no longer valid. Some of the examples are roller coasters, cars on hilly roads, etc. 2. The minimum velocity given to the mass at it's equilibrium position so that it can complete vertical circular motion is /Kgl. calculate the minimum value of v 0 so that the 2 days ago · The motion in a vertical circle is considered nonuniform as the influence is observed the most at the lowest and the least at the highest point of the path. At the top of a circular trajectory the ball momentarily moves in the horizontal direction while it accelerates downwards in the vertical direction. = ( − 2 − 2. Remember, acceleration is change in velocity, and a velocity is made up of speed and direction. Step 2: Find the minimum speed of the object (the speed at the top of the circle) using the formula vmin=√rg v min = r g . (g = 9. Now in order to move in circular motion, there must be an inward force i. Mar 28, 2024 · 4. 5 m. 18 (a) A particle is moving in a circle at a constant speed, with position and velocity vectors at times t t and t+Δt. Jul 14, 2015 · To complete the case, I am adding the minimum initial velocity which we get from $$\dfrac{m(u^2 - v ^2)}{2} = mgh \implies u = 2\sqrt{gR}$$. Radian measure and arc length can be applied to the study of circular motion. Feb 15, 2024 · Motion In A Vertical Circle : Consider a particle of mass m attached to a string of length r as shown in Figure. T = m (v 2 /r) - mg. This is why you feel heavier at the bottom and lighter at the top. A thin circular disc of mass M and of radius a / 4 is pivoted on this rod with its center at a distance a / 4 from the free end so that it can rotate freely about its vertical axis, as shown in the figure. Δs) • Angle in “radians” ≡ (arc length / (radius r) Note that v = r (2π/T) = r ω [m/s], and therefore v is proportional to the radius of the circle. The vector Δ→v points toward the center of the circle in the limit Δt → 0. 4414 min. Key Points. Circular motion, centripetal acceleration, in a uniform gravitational field Problem : Find the minimum rotational frequency (i. 00 cm, so the initial position does not equal the amplitude x 0 = + A x 0 = + A. Suppose a body is tied to a string and rotated in a vertical circle as shown. Considered the situation as shown in the figure. A particle of mass mis attached to a light rod of length 1 Other end of the rod is hinged to wall. Nov 21, 2023 · For an object tied to a string as it moves in a vertical circular motion, the tension at the bottom can be calculated using the equation below: Tension at the bottom of the circle = m (vB)^2/r Click here👆to get an answer to your question ️ A particle is attached at one end of massless rod whose other end is fixed at O as shown in figure. Critical Velocity. Note that, unlike speed, the linear velocity of an object in circular motion is constantly changing because it is always changing direction. A body of mass m hangs at one end of a string of length I, the other and of which is fixed. Length of rod is ℓ . Dec 22, 2016 · 3. If we wanted to calculate the minimum or critical velocity needed for the block to just be able to pass through the top of the circle without the rope sagging then we would start by letting the tension in the rope approaches zero. , David says that the speed of the ball in the outermost right position will increase compared to the speed in the top position. As the projectile moves upwards it goes against gravity, and therefore the velocity begins to decelerate. Also called radial acceleration. A circular motion is said to be uniform if an object covers equal angular displacement in equal interval of time. Sep 1, 2015 · The necessary centripetal force is T − mgcosθ = mv2 R. Also known as Centripetal Motion, Uniform Circular Motion refers to objects moving in a circular path with A body of mass m is suspended from a string of length l. A block of mass m is attached to two unstretched springs of spring constants k 1 and k 2 as shown in figure. This week, we will use radians to measure the angles, so all angles will have units of radians, angular velocity will have units of radians/s, and angular acceleration will have units of radians/s\(^2\). If the speed is larger, then the normal force will be positive and will combine with gravitation to result in the centripetal force. 1. Find the radius of the circular path and the time it takes to complete one circular orbit in terms of the given quantities and g . ) Q. Sep 12, 2022 · The data are collected starting at time t = 0. Mass of the body, m = 2 kg. 0 + m g = m v min 2 r m g = m v min 2 r v min 2 = g r v min = g r This is the minimum velocity also called as Another identical ball is thrown vertically downwards such that its surface remains just in contact with thread during downward motion and collides elastically with the suspended ball. Velocity at midway position: Equation (6) represents minimum velocity of a body at midway position, so that it can safely travel along vertical circle. 8 The data are collected starting at time t = 0. In principle, this is motion in two dimensions, as a circle is necessarily in a two dimensional plane. The block is displaced towards right through a distance ' x ' and is released. Time Period (T) Time period (T) is the time taken by the ball to complete one revolution. Δ t → 0. A light rod of length L is hanging from the vertical smooth wall of a vehicle moving with acceleration 3 g along the horizontal plane having a small mass attached at its one end and is free to A particle of mass m attached to a string of length l is describing circular motion on a smooth plane inclined at an angle α with the horizontal. To find the minimum velocity at the bottom-most point, we find the minimum velocity at the uppermost point. Circular Motion in a vertical plane Nov 25, 2020 · 1. This is consistent with the initial horizontal velocity of 20 m/s. 12 Object in a circular orbit on inside of a cone The gravitational force is constant. (b) Velocity vectors forming a triangle. e. At the top, tension is given by T = mv T 2 /R - mg, where v T = speed of the particle at the top. Find the minimum height h, so that ball will just complete the circular motion on the track (all surfaces are smooth). A block is released from height h on a smooth track. Sep 12, 2022 · Figure 4. The apex half-angle of the cone is θ as shown in Figure 9. Sep 7, 2022 · This uniform circular motion calculator operates in two modes: Calculating time period, frequency, and angular velocity : Enter any one of these parameters with appropriate units. 12. So the minimum velocity needed at the highest point to complete a vertical circle is expressed as √ (gr) Also, the instantaneous velocity can be read off the velocity graph at any moment, but more steps are needed to calculate the average velocity. The calculator can determine the remaining two parameters automatically. For any velocity above this minimum, we can use conservation of energy to Jul 20, 2022 · The axis of the cone is vertical and gravity is directed downwards. Causes an object to change its direction and not its speed along a circular pathway. Jun 30, 2021 · Problem 1: A stone weighing 2 kg is whirled in a vertical circle at the end of a rope of length 1 m. A particle is given minimum velocity at lower most point to complete vertical circular motion about O . Objects moving in a circle are under the constant influence of a changing force, since their trajectory is not in a straight line. 4. This is the condition for "weightlessness" in any curved motion in a vertical plane. Definition of Vertical Circular Motion. centripetal force perpendicular to the instantaneous velocity. For a mass moving in a vertical circle of radius r = m, if we presume that the string stays taut, then the minimum speed for the mass at the top of the circle is (for g = 9. We know that, v= R ω. However, since the object is constrained to move along the circumference of the circle, it can be thought of (and treated as) motion A light rod of length L, is hanging from the vertical smooth wall of a vehicle moving with acceleration 3 g having a small mass attached at it's one end is free to rotate about an axis passing through the other end. This step helps you to devise a strategy for your solution. c) topmost position to just complete the circle. A motor cyclist rides in a vertical hollow sphere of radius 5 m. Then, the critical velocity is 2√gl. Go the other way you get: −m v2 r + m g + T = 0 − m v 2 r + m g + T = 0. ) = −ω2. Its (a) velocity remains constant (b) speed remains constant (c) acceleration remains constant (d) tangential acceleration remains constant. Find the value of K. 5. Vertical circular motion (VCM) is a special type of circular motion in which the body travels in a vertical plane. class-12 Aug 13, 2020 · So with the string the ball has to move fast enough that no pushing up is required from the string when the ball is at the top, but this is not true in the case of the rod. The two triangles in the figure are similar. Find net force on the particle when it is at position P . 00s, but the initial position is near position x ≈ − 0. Thus, the horizontal displacement is 20 m at 1 second, 40 meters at Sep 12, 2022 · The vector between them is the displacement of the satellite. Due to this, the centripetal force on the particle and hence the tension We will discuss specifically circular motion and spin. The minimum speed given to the particle so that the rod performs circular motion in a vertical plane will be : [length of the rod is l, consider masses of both rod and particle to be same] m, l (A) 5ge (B) 4ge (D) none of these (C) 14. The minimum velocity given to the mass at its equilibrium position with respect to vehicle so that it can complete vertical circular It means all bodies (whether an iron ball or a piece of paper), when dropped (u = 0) from same height should fall with the same rapidity and should take the same time to reach the earth, i t is the minimum velocity given to the particle at the lowest point to complete the circle. Sep 15, 2022 · The minimum velocity given to the mass at it's equilibrium position so that it can complete vertical circular motion is KgL . What is the minimum horizontal velocity that should be given to the body at its lowest position so that it may complete one full revolution in the vertical plane with the point of suspension as the centre of the circle? m (v 2 /r) = T + mg. Thus, if we give the pendulum a spees less that the minimum, it will not be able to undergo a circular motion and starts to oscilate. 0 = m (v 2 /r) - mg. If the bead is constrained to move in a vertical circle (because it is in a pipe or on a wire or attached to the centre by a rigid rod, for example) then the only condition for completing a whole circle is that its speed at the top of the circle is greater than or equal to zero. 2) Non uniform circular motion:-. The path is a circle (radius r, circumference 2πr). v. To study uniform circular motion, we define the following terms. applying principle of conservation of energy, total mechanical energy at L = Total mechanical energy at H ∴ 1 2 m v 2 L = 1 2 m v 2 H + m g (2 l) but, v 2 H = g l ∴ 1 2 m v 2 l = 1 2 m (g l) + 2 m g l ⇒ v 2 L = 5 g l ⇒ v L = √ (5 g l) Hence, for looping the vertical loops The acceleration vector is. This minimum velocity is the one such that the centripetal force is equal to the force of gravity. This force is known as centripetal force. Aug 19, 2015 · 1. A particle is attached to the lower end of a uniform rod which is hinged at its other end as shown in the figure. 8 m/s 2) m/s. l. Circular motion is classified into two types: uniform circular motion and non-uniform circular motion. => mv T 2 /R = T + mg A uniform disc of mass m and radius R is hanging from a rigid support and is free to rotate about a horizontal axis passing through its center in vertical plane as shown. Vertical Circular Motion Using a String. Before talking about Newton's third law, it's very important that we look at how circular motion is affected in accordance with Newton's first 2 laws. It is given a horizontal velocity so that the string would just reach where it makes an angle of 3 0 o with the vertical. 00 s, t = 0. Find the value of `K`. A ball of mass m is released from rest at A as shown in the figure. An insect of mass m falls vertically and hits the disc at a point at horizontal diameter with a velocity v 0 and sticks on it. In the case we are discussing here, velocity of the body is different at different points. Two point mass m are connected the light rod of length l and it is free to rotate in vertical plane as shown. ) Acceleration pointed towards the center of a curved path and perpendicular to the object’s velocity. m (v 2 /r) = mg. We take the radius of Earth as 6370 km, so the length of each position vector is 6770 km. the number of rotations per second, not the angular frequency) required to rotate a bucket containing 4 liters of water in a circular path in a vertical plane at an arm's length (about 70 cm) without spilling water. May 27, 2023 · Step 1: Identify the radius of the vertical circular motion, r in meters, and the approximation of the centripetal acceleration due to gravity, g in meters per second squared. It can be uniform, at constant speed, or non-uniform with a changing rate of rotation. 4: Circular Motion- Linear and Angular Speed. The minimum velocity given to the mass at its equilibrium position with respect to the vehicle so that it can complete vertical circular motion is Q. Aug 26, 2021 · Equation (5) represents minimum velocity at the lowest point, so that body can safely travel along vertical circle. Let the particle be whirled in a vertical circle (of radius r), then the speed of the particle is different at different points of the vertical circular path. A particle is projected from lowest position with minimum velocity such that particle just can complete vertical circular motion, Ratio of normal force acting on the particle at lowest position to highest postion is 11x (0 = cos' and width of tube is small). Mar 26, 2016 · At the minimum speed that will prevent the object from falling, the normal force is 0 and the gravitation is the centripetal force. In the previous section, we defined circular motion. v = √R m(T − mgcosθ) |θ = π ≠ 0 In order to have the critical case or the minimum velocity for looping the circle (T − mgcosπ) must be A part of inner surface of a vertical smooth, fixed circular tube of radius 5m is removed as shown. Choose positive up and you get: m v2 r − m g − T = 0 m v 2 r − m g − T = 0. Uniform Circular Motion. Circular motion is when an object moves in a circular path. Let us assume the ball takes 3 seconds to complete one A rod (mass 3kg, length = 1 meters) is hanging vertically, hinged smoothly at its one end. 1: (a) A particle is moving in a circle at a constant speed, with position and velocity vectors at times t and t + Δt. If ‘r’ is the radius of the circle of motion, then in time ‘T’ our ball covers a distance = 2πr. 0 s to complete the table. 00 s, but the initial position is near position x ≈ − 0. Calculate the minimum horizontal velocity is given to mass so that it completes the circular motion in vertical lane. Page ID. We often consider the motion of an object around a circle of fixed radius, R. In physics the average speed of an object is defined as: So suppose that an object moves along a circle of radius \ (r \), traveling a distance \ (s \) over a period of time \ (t \), as in Figure 4. If the car is to just maintain contact with the track at the top of the loop, what is the minimum value for its velocity at this point? Dec 10, 2023 · The minimum speeds of $\sqrt {4gl}$ and $\sqrt {5gl}$ apply in two different situations. The velocity is the time derivative of the position, which is the slope at a point on the graph of position versus time. See also What is u mean in physics? Correct answer: Explanation: Remember, when working with circular motion, the velocity is ALWAYS tangential to the circle. . Paul D’Alessandris ( Monroe Community College) This page titled 06. For the bucket, the normal force points from the b Circular Motion. 77m/s The net force acting on a mass that is travelling in a vertical circle is composed of the force of gravity and the tension in the string. Sep 16, 2022 · 4. But when we derived formulas for centripetal acceleration in earlier videos, we assumed that the speed is constant. Gravity, g = 9. It means all bodies (whether an iron ball or a piece of paper), when dropped (u = 0) from same height should fall with the same rapidity and should take the same time to reach the earth, i t is the minimum velocity given to the particle at the lowest point to complete the circle. The change in speed has implications for radial ( centripetal ) acceleration. Find the minimum value of v (in m/sec) so that the rod completes its vertical circular motion subsequently. Now, the only force acting on the particle is the force of gravity Minimum Velocity required to Loop in the Vertical Circle. Find the velocity of a stone at a) lowest position b) midway when the string is horizontal c) topmost position to just complete the circle. Minimum velocity (vo) that should be given to the particle in lowest position so that it completes a vertical circle OR (1) V5g/ (3) Vagi (2) 1391 (4) Vog Calculate the time period of its oscillation. Assume that both the rod and disc have uniform density and they remain horizontal during the motion. Aug 13, 2020 · We can now determine angular acceleration, radial acceleration, and tangential acceleration. Δ v = v r Δ r. If the suspended ball just completes vertical circle after collision, calculate the velocity (in cm/s) of the falling ball just before collision : (g = 10 m s − 2) In vertical circular motion, the ratio of kinetic energy of a particle at highest point to that at lowest point is _____. To continue vertical circular motion, v M = \(\sqrt{3rg}\). . consider masses of both rod and particle to be same. 7:53. Find minimum angular speed required so that it does not loose contact with the sphere at the highest point. The velocity is the time derivative of the position, which is the slope at a point on the graph of Sep 14, 2023 · Vertical Circular Motion | Minimum Velocity To Complete a Circle | Complete Circular Motion JEE |Vertical Circular Motion | Minimum Velocity To Complete a Ci Jan 22, 2019 · For driven motion, there is no velocity too small ( or too large) for the motion to be circular. Solution: Given: Radius of circular path, r = 1 m. You may assume the planet moves in an -plane. Centripetal force is not something new. If the path is circular, the speed is uniform, and the string is attached at the center of the motion, then a similar argument shows that the tension in the string must be nonuniform. Centripetal acceleration ( a c. There are two possibilities: 1) the radius of the circle is constant; or 2) the radial (centripetal) force is constant. At highest point C, tension is minimum. t + Δ t. A particle can travel in a circle and speed up or slow down, showing an acceleration in the direction of the motion. Determining the radius, speed, and acceleration : Provide the circular motion's time period SI units of radians s. Figure 9. Eventually the vertical velocity will reach zero, and the projectile is accelerated downward under gravity immediately. The vector Δ→v Δ v → points toward the center of the circle in the limit Δt→ 0. When a ball is tied securely to a cord, it will move in a circle. For the particle to reach the highest point its velocity at the lowest point should exceed. It is denoted by ‘T’. This change in direction is the acceleration, called A simple pendulum of mass m is performing vertical circular motion with its velocity at the highest point being V = √ 2 g l where l is the length of the string. Any other circular motion will require a larger angular velocity. Equations for VCM. The vector Δ→v Δ v → points toward the center of the circle in the limit Δt→0. Find the tension in the string when it reaches the lowest point. What this means is that the minimum speed is reached for $\theta=0$, where \omega_min=\sqrt{L/g}. Our ball is being swung in a circle, so circular motion is a good approach to use. Examples of circular motion include a race car speeding around a circular curve, a toy attached to a string swinging in a circle around your head, or the circular loop-the-loop on a roller coaster. Such a motion is therefore called non-uniform circular motion. Find the velocity of a stone at: a) the lowest position . This equation can be derived from the centripetal force equation, Fc = mv²/r, and setting the Figure 4. Consider a particle attached to the centre of a circle via an inextensible string undergoing vertical circular motion. Consider the mass of a body m and the magnitude of the centripetal force f c, f c = mass × acceleration. If the initial velocity u u is such that 2gl−−−√ < u < 5gl−−−√ 2 g l < u < 5 g l, the tension becomes 0 at a point where θ θ is obtuse. Circular motion does not have to be at a constant speed. The simplest case of circular motion is uniform circular motion, where an object travels a circular path at a constant speed. If the centripetal force is absent then the circular motion is not possible. Vertical Circular Motion: An object is undergoing vertical circular motion if it moves along a vertical circle (a circle with a top and a bottom). But if the speed is lower than the falling threshold, the normal force will be Two point mass m are connected the light rod of length l and it is free to rotate in vertical plane as shown. It is an example of non-uniform circular motion. If the string is connected by some low-friction method to In case of vertical circular motion this is the minimum velocity that a body must be given at the lowest position to complete a vertical circle. So the velocity required to reach Y can be found out by conserving mechanical energy, \ (\begin {array} {l}E_x (Energy\, at \, X Jan 16, 2020 · Numerical Problems on Motion in Vertical Circle: Example – 01: A stone weighing 1 kg is whirled in a vertical circle at the end of a rope of length 0. vecF_"net" = vecF_g+vecT Since this net force results in centripetal motion (the mass travels in a circle at constant speed), the net force is acting as a centripetal force: vecF_c=vecF_g+vecT To "stay in motion" as you say, we mean the mass must A particle is attached to the lower end of a uniform rod which is hinged at its other end as shown in the figure. “Uniform” means constant speed v = 2πr / T, where the period T is the time to go around the circle once. 3: Two position vectors are drawn from the center of Earth, which is the origin of the coordinate system, with the y-axis as north and the x-axis as east. 8m/s 2) Explain the term sphere of death. Note: In case the particle is attached with a light rod of length l, at the highest point its minimum velocity may be zero. Q. If the tension is zero at this point, then the weight of the body provides necessary centripetal force to loop in a vertical circle. In a circular motion, the direction of velocity at any point is: Q. Therefore, f c = m R ω2. b) midway when the string is horizontal . The minimum velocity given to the mass at its equilibrium position with respect to vehicle so that it can complete vertical circular motion respect to vehical) is `sqrt(KgL)`. The minimum speed given to the particle so that the rod performs circular motion in a vertical plane will be : (length of the rod is l. Each of these functions could be evaluted at t 1 = 0 s and t 2 = 10. Example 1: A planet of mass 1010kg is in horizontal circular motion around a star and has a position vector ( 3cos + 2 ) km given by 3sin − 1 . In non- uniform circular motion, the size of the velocity vector (speed) changes, denoting change in the magnitude of velocity. non hazara ar negative for completing the May 21, 2023 · Step 1: Identify the radius of the vertical circular motion, r in meters, and the approximation of the centripetal acceleration due to gravity, g in meters per second squared. The velocity of anybody undergoing motion in a vertical circle is given by v = u2 − 2gh− −−−−−−√. The tension in the string at mean position is Oct 23, 2020 · If the ball is attached to a hard support then it is constrained to move along the circular path, so no matter what the speed, as long as it is non-zero, circular motion will be achieved. In uniform circular motion, the particle executing circular motion has a constant speed and the circle is at a fixed radius. It is moving at different speeds at different times, so we will use nonuniform circular motion. It is the minimum velocity given to the particle at the lowest point to complete the circle. The speed of the object is at a minimum when the Nov 21, 2009 · The minimum speed for vertical circular motion can be calculated using the equation v = √ (rgtanθ), where v is the minimum speed, r is the radius of the circular path, g is the acceleration due to gravity, and θ is the angle of the circular path. 00 cm, so the initial position does not equal the amplitude x 0 = + A. At. Apr 8, 2020 · Therefore the magnitude of the velocity vector isn't a constant, and the circular motion is not uniform. (All surfaces are smooth. Nov 4, 2014 · First I thought the tension at the top most position must be greater than zero, then I thought that the tangential velocity at the top must be greater than zero, because then even if the tension becomes zero as soon as the object pulls it due to its speed a new tension arise and so it will keep going on a circular motion. The tension in the string is what keeps the ball moving in a circle Sep 21, 2017 · Critical velocity formula is expressed as V1 = √ (gr) where g is the acceleration due to gravity and r is the radius of the vertical circular path being traversed by the object. Consider a ball of mass Find the minimum height h so that ball B just completes the circular motion of the surface at C. Nonuniform Circular Motion. What minimum velocity should be given to the particle at rest from its equilibrium position so that it completes a full circle in vertical plane? Calculate the maximum and minimum tension in the thread in its circular motion in vertical plane. For right now, let's look at how UCM (Uniform Circular Motion) works. A key difference between the car and water bucket examples: The normal is always up for the car. 12. The normal force equals your apparent weight. This means that, even though the speed is constant, the direction is always tangent to the edge of the circle. Figure 4. Examples of circular motion include: an artificial satellite orbiting the Earth at constant height, a stone tied to a rope Jul 21, 2023 · A light rod length L, is hanging from the vertical smooth wall of a vehicle moving with acceleration √3g having a small mass attached at its one end is free to rotate about an axis passing through the other end. cos sin. 00 cm x ≈ − 0. 5ge Circular motion is a movement of an object in a circle. 80 cm ≠ 3. And in the case of vertical circular motion, it seems quite intuitive to me. The maximum height of a object in a projectile trajectory occurs when the vertical component of velocity, vyvy, equals zero. Any lower and gravity will pull the object down and out of the loop, any higher and a faster velocity would be required to generate it Furthermore, since there is no horizontal acceleration, the horizontal distance traveled by the projectile each second is a constant value - the projectile travels a horizontal distance of 20 meters each second. Find the linear speed of the particle. For the object to move in a circle, the direction of its velocity must change constantly. This happens because of circular motion. The tendency of the string to become slack is maximum when the particle is at the topmost point of the circle. The work done in uniform circular motion is zero because the angle between force and displacement is 90ο. A roller coaster car of mass 100 k g is on a track that forms a circular loop of radius R = 10 m in the vertical plane. The minimum velocity at the topmost point is thus infinitesimally greater than $0$. [AL] Guide students in seeing that the area under the velocity curve is actually the position and the slope represents the rate of change of the velocity, just as the slope of the position line The position vector of a particle in a circular motion about the origin sweeps out equal area in equal time. So the minimum initial velocity must be infinitesimally larger than $2\sqrt{gR}$. ‍. If the circle below represents the path of the yo-yo, and it moves in a clockwise direction, then the velocity In case of vertical circular motion this is the minimum velocity that a body must be given at the lowest position to complete a vertical circle. The Kinematics of Circular Motion is shared under a CC BY-NC-SA license and was authored May 1, 2021 · 1) Uniform circular motion:-. Derive expressions for the linear velocity at the lowest position, mid-way position and top-most position for a particle revolving in a vertical circle, if it has to just complete circular motion without string slackening at the top. It really doesn't matter whether you choose up or down as positive. uq zy nn af dp mt ye ho ex cw