A "swing ride" is shown in the figure. Calculate the necessary angular velocity w for the swings to assume an angle 0 = 22° with the vertical. Neglect the mass of the cables and treat the chair and person as one particle.
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- After all the metal has unwound from the roller, the student measures the radius R and the angular speed wo of the roller to be 25 cm and 20 rad/s respectively. Observed from the side, the roller rotates counterclockwise, as shown. A piece of clay of mass m strikes the very bottom edge of the roller with a horizontal velocity v = 4.0 m/s. The clay sticks to and rotates with the roller. The clay-roller system then rotates with a final angular velocity wi. (f) Is wi greater than, less than, or equal to wo? Justify your answer.Consider the father pushing a playground merry-go-round. He exerts a force of 250 N at the edge of the 50.0-kg merry-go-round, which has a 1.50-m radius. Calculate the angular acceleration produced (a) when no one is on the merry-go-round and (b) when an 18.0-kg child sits 1.25 m away from the center. Consider the merry-go- round itself to be a uniform disk with negligible friction.a 0.400 kg ball is shot directly upward at initial speed 69.6 m/s. What is its angular momentum about P, 2.50 m horizontally from the launch point, when the ball is (a) at maximum height and (b) halfway back to the ground? What is the torque on the ball about P due to the gravitational force when the ball is (c) at maximum height and (d) halfway back to the ground?
- An object with mass m is attached to a string with initial length R, and moves on a frictionless table in a circular orbit with center C as shown in the figure. The string is also attached to the center, but its length is adjustable during the motion. The object initially moves with velocity v and angular velocity w Top View Given: m = 375g, v = x m/s, R = 50 cm If the length of the string is shortened from R to rR/2 while the mass is moving, the new period of the object will be the SI unit). rad/s (chooseA parent exerts a force of F = 115 N tangent to playground merry-go-round for t = 1.84 seconds. The merry-go-round has a radius of 3.50 m and moment of inertia I = 325 kg×m2. If it starts from rest, find the: a) angular acceleration (a), b) tangential acceleration (at), c) final angular speed (wf), d) final kinetic energy (KER) Equations: t = Fr^ t = Ia at = r×a wf = wi + at KEr = ½ Iw2The figure below shows a ball with mass m = 0.322 kg attached to the end of a thin rod with length L = 0.454 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. The rod is held horizontally as shown and then given enough of a downward push to cause the ball to swing down and around and just reach the vertically up position, with zero speed there. (a) What initial speed must be given the ball so that it reaches the vertically upward position with zero speed? m/s (b) What then is its speed at the lowest point? m/s (c) What then is its speed at the point on the right level with the initial point? m/s
- Please asap ?A track is mounted on a large wheel that is free to turn with negligible friction about a vertical axis (figure below). A toy train of mass m is placed on the track and, with the system initially at rest, the train's electrical power is turned on. The train reaches speed 0.20 m/s with respect to the track. What is the wheel's angular speed if its mass is 1.2m and its radius is 0.45 m? (Treat it as a hoop, and neglect the mass of the spokes and hub.) rad/sHow much work is done by the motor in a CD player to make a CD spin, starting from rest? The CD has a diameter of 12.0 cm and a mass of 15.8 g. The laser scans at a constant tangential velocity of 1.20 m/s. Assume that the music is first detected at a radius of 22.0 mm from the center of the disk. Use the tangential velocity of the the laser and the radius at which music is first detected to determine the angular velocity of the disc. Ignore the small circular hole at the CD’s center.
- Question in pic.A solid sphere with radius 0.11 m and mass 2.8 kg rolls without slipping around a track that has been bent into avertical circle of radius R = 2 m. (Note that the center of mass of the ball moves in a circle with a radius (R − r),as shown by the dashed line in the figure). At the top of the track, the ball moves with speed 7.6 m/s. What is thespeed of the ball at the bottom of the track?An air puck of mass 0.17 kg is tied to a string and allowed to revolve in a circle of radius 1.4 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of 0.8 kg is tied to it (Fig. P7.25). The suspended mass remains in equilibrium while the puck on the tabletop revolves. Figure P7.25 (a) What is the tension in the string? N(b) What is the force causing the centripetal acceleration on the puck? N(c) What is the speed of the puck? m/s