Example F: A disk with a mass M, a radius R, and a rotational inertia of I= 2 MR2 is attached to a horizontal spring which has a spring constant of k as shown in the diagram. When the spring is stretched by a distance x and then released from rest, the disk rolls without slipping while the spring is attached to the frictionless axle within the center of the disk. Calculate the linear velocity of the disc. wwwwww

A uniform ball of radius 0.1 m and mass 1 kg is released from rest on a no-slip surface, as shown in the figure, at a height of 2m. a. If the ball’s speed at the bottom is 5.29 m/s, what is its rotational kinetic energy? b. What is its translational kinetic energy? c. If there were no friction, what speed would it reach the bottom with?

Two boxes are connected to a cord, and the cord is hung over a pulley connected to the ceiling, as shown in the figure below. m1 The masses of the boxes are m₁ = 16.0 kg and m₂ 10.0 kg, the mass of the pulley is M = 5.00 kg, and the radius of the pulley is R = 0.300 m. Box m₂ is initially on the floor, and box m₁ is initially 5.00 m above the floor when it is released from rest. The pulley's axis has negligible friction. The mass of the cord is small enough to be ignored, 1 and the cord does not slip on the pulley, nor does it stretch. = At ₂ MOR (a) How much time (in s) does it take box m₁ to hit the floor after being released? At ₁ = mq S (b) How would your answer to part (a) change if the mass of the pulley were neglected? (Enter the time, in seconds, it takes box m₁ to hit the floor if the mass of the pulley were neglected.) = S

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