A thin square plate of mass m rotates on a smooth surface with an angular velocity of about its mass center. The hook then strikes the peg at P and the plate starts to rotate about point P with no rebound. What is the plate's angular velocity after impact, and the speed vg of the mass center of the plate?
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- A disk of radius R=27 cm released from rest down a ramp. It rolls without slipping and its center of mass goes down by h=0.99 meters when it reaches the ground level. Find the center-of-mass speed of the disk right after it reaches the ground level. Enter your answer in m/s.A 200-kg, 2.0-m-radius, merry-go-round in the shape of a flat, uniform, circular disk parallel to level ground is rotating at 1.2 cycles/second about an axis through its center of mass and perpendicular to the ground. A 50-kg boy jumps onto the edge of the merry-go round and lands at a fixed point. What is the angular velocity of the merry-go-round after the boy lands on it? Hint: = (1/2)mR2 where m is the mass of the disk and R is the radius of the disk.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?
- A rod 2-meter long rod is initially at rest and is fixed on its right side, which acts as its axis of rotation. A 200 N force acts on the rod 0.5 meters away from the axis of rotation downward and a 100 N force acts on the rod 1.5 meters away from the axis of rotation upwards. Calculate the angular momentum of the rod after 2 seconds have past.A uniform, thin, spherical shell of radius, R, and mass, m, is rolling without slipping or sliding on a level surface. If the center-of-mass velocity of the ball is vCM what is the total kinetic energy of the 2 MR? ball? Hint: cm,shell VCM IR Contact Point O a. 1my? ,2 ст 2 b. 7 mv2 10 ст С. ту2 ст d. 5 ,2 -mv ст 3 е. mv2 4The figure shows multiple solid disks with uniform mass distribution that are spinning about its center. The mass of the disks are the same, but they have different radii, as shown. Rank the disks by the amount of energy needed to spin the disk so that the outer edge of the disk has linear velocity v, from greatest to least. Explain your reasoning. A B с
- A thin rod with a length of 4.0 m and a mass of 4.2 kg is initially at rest. It is capable of spinning around a frictionless axle that goes through the top of the rod. A 2.5 kg mass of clay collides perfectly idealistically with the bottom of the rod. The clay was traveling perfectly horizontally with a speed of 12 m/s before the collision. How fast will the rod with the clay attached to it rotate around the axle in radians per second? The only external force on the clay/rod system come from the axle, which exerts no torque about itself.A 3.0-kg mass slides on a frictionless horizontal surface with a speed of 3.0 m / s when it collides with a 1.0-kg mass initially at rest as shown in the figure. The two masses stick to each other and slide on a frictionless circular wheel portion of radius 0.40 m. At what maximum height h, above the horizontal, do the masses reach? Answers: a) 0.18 m b) 0.15 m c) 0.21 m d) 0.26 m e) 0.40 mConsider five equal mass objects all with the same non-zero kinetic energy. Unless otherwise stated assume the axis of rotation is through the center-of-mass. Assume all densities are uniform or constant. Order these objects from lowest angular velocity (1) to highest angular velocity (5). Rod of length 2R (axis perpendicular to rod). Solid sphere of radius R. Solid disk of radius R (axis perpendicular to plane of disk). Hoop of radius R (axis perpendicular to plane of disk). Rod of length 2R (axis perpendicular to rod, axis through END of rod).
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