Question

1.) Rotational Motion

a.) A thin solid disk of radius R = 0.5 m and mass M = 2.0 kg is rolling without slipping on a horizontal surface with a linear speed v = 5.0 m/s. The disk now rolls without slipping up an inclined plane that is at an angle of 60 degrees to the vertical. Calculate the maximum height that the disk rolls up the incline.        

A. 5.1 m    

B. 2.6 m    

C. 2.9 m    

D. 3.1 m    

E. 1.3 m

b.) Water is drawn from a well in a bucket tied to the end of a rope whose other end wraps around a solid cylinder of mass 50 kg and diameter 25 cm. As this cylinder is turned with a crank, the rope raises the bucket. The mass of a bucket of water is 20 kg. Someone cranks the bucket up, lets go of the crank, and the bucket of water falls down to the bottom of the well. Without friction or air resistance, what is the angular acceleration of the 50-kg cylinder?

A. 1.1 × 10² rad/s²     

B. 3.6 rad/s²     

C. 35 rad/s²     

D. 63 rad/s²     

E. 17 rad/s²

The answers are B. 2.6 M & C. 35 rad/s² but I need to know how to calculate them. Thank you!

Answer 1