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- 1) A solid sphere and a hollow cylinder are both rolling without slipping along a smooth horizontal surface at a translational speed of v = 6.35 m/s. They then encounter a hill. hmax a) Which object reaches a larger maximum height above the level ground? b) What is the maximum height the object from Part A reaches?A hollow cylinder with mass M = 3 kg and radius R = 0.6 m rolls down a 4 m high hill. What would be the speed ofthe cylinder when it reaches the bottom of the hill?A uniform solid sphere of mass 25 kg and radius 0.2 m rolls without slipping along a ramp 5.0 m long and inclined 30° with the horizontal . Find the angular velocity of the sphere at the bottom of the ramp.
- The center of the cylinder is moving to the left with constant velocity vo. Determine the angular velocity and the angular acceler- ation a of the bar. Neglect the thickness of the bar.A solid cylinder with a mass of (5 kg) and a radius of (0.2 m) (I =12MR2) is initially rolling along a flat plane with a linear velocity of (10ms). The cylinder then comes to the edge of a ramp that is inclined by (34degrees) to the horizontal and begins to roll up the ramp. How high above the flat plane does the cylinder reach before it starts to roll back down?A uniform solid sphere of radius r is placed on the inside surface of a hemispherical bowl with radius R. The sphere is released from rest at an angle θ to the vertical and rolls without slipping (Fig.). Determine the angular speed of the sphere when it reaches the bottom of the bowl.
- The drum has a radius of 25cm. (a) Find wmin, the minimum angular speed at which the drum needs to rotate, so that a t-shirt can remain stuck at some point on the curved edge of the drum as it rotates (hint: in particular, the t-shirt should remain stuck to that point on the drum even when it gets to the top of the drum). (b) Find the linear speed of the t-shirt if the drum rotates at the minimum angular speed that you found in (a). (c) Suppose that the drum starts from rest and reaches the angular velocity that you found in (a); 10 seconds after starting. Assuming that the angular acceleration is constant within these 10 seconds, find the number of rotations made by the drum in this time.A smooth rod of mass M, length L=2 (m), is rotated at one end with a constant angular velocity w = 3 (rad/s) as shown in the figure. Att =0pan-insest of m=0.02 (kg) moves from point O to the other end of the rod with a cons tant velocity of v 4 (m/s) and stops at the end af rod. The angular velocity of the rod remains constant during the movement. Find the torque acting on the rod in (N.m) when the insect reaches to the end of rod (just before it stops). M x = L A) 0.48 В) 0.16 C) 0.72 D) 0.24 E) 0.96A bob attached to a string of length 2 m, is displaced by an angle of 8° and then released from rest. The maximum angular acceleration, e"max, is: (Take g = 10 m/s?) O 0.42 rad/s² 0.7 rad/s? 0.8 rad/s? 0.56 rad/s? 0.25 rad/s2