The 47-kg flywheel has a radius of gyration of ko = 300 mm about its center of mass. (Figure 1) Figure Part A M = (9 0¹/2) N.m 1 of 1 If it is subjected to a torque of M = (90¹/2) N. m, where is in radians, determine its angular velocity when it has rotated 3 revolutions, starting from rest. Express your answer to three significant figures and include the appropriate units.

A 1.756-kg sphere of radius 0.31 m is rotating about an axis through its center at 24.843 rev/s with the angular velocity in the +z direction.  A torque 11.573N∙m acts on the sphere about the center of the sphere in the +x direction.  What is the angular acceleration, in rad2/s, of the sphere? (Isphere = 2/5 MR2)

A cylinder with a radius of 13 meters and a mass of 8.5 kg rolls without slipping, traveling at 6 m/s. What is the total K.E. of the cylinder in J?

A playground merry-go-round has a mass of  133kg and a radius of  1.82m and it is rotating with an angular velocity of  0.424rev/s. What is its angular velocity after a 29-kg child gets onto it by grabbing its outer edge? The child is initially at rest.

A playground uniform merry-go-round has a mass of 110 kg and a radius of 1.90 m and it is rotating at a rate of 40 revolutions per minute. a) What is its angular velocity [ in rad/s] after a 20-kg child gets onto it by grabbing its outer edge? The child is initially standing on the ground. b) What is the new angular velocity [in rad/s] after the child moves to the center of the merry-go-round?

In the figure here, a cylinder having a mass of 4.3 kg can rotate about its central axis through point O. Forces are applied as shown: F1 = 4.7 N, F2 = 3.6 N, F3 = 6.1 N, and F4 = 2.3 N. Also, r = 5.3 cm and R = 15 cm. Taking the clockwise direction to be negative, find the angular acceleration of the cylinder. (During the rotation, the forces maintain their same angles relative to the cylinder.)

A 1.0 kg ball and a 2.0 kg ball are connected by a 1.1-m-long rigid, massless rod. The rod is rotating cw about its center of mass at 20 rpm. What torque will bring the balls to a halt in 5.6 s? Express your answer in newton-meters to two significant figures. ΠΑΣΦ T = ? N.m

Problem 1: A small rubber wheel is used to drive a large pottery wheel. The two wheels are mounted so that their circular edges touch. The small wheel has a radius of 6.5 cm and accelerates at the rate of 7.5 rad/s2 , and it is in contact with the pottery wheel (radius 24.0 cm ) without slipping. Part A Calculate the angular acceleration of the pottery wheel.   Part B Calculate the time it takes the pottery wheel to reach its required speed of 70 rpm .