\ A uniform solid cylinder of mass

M

and radius

R

is mounted on frictionless bearings about a fixed axis through the center of the cylinder. The moment of inertia of the cylinder about the axis is

(1)/(2)MR^(2)

. A block of mass

m

, suspended by a cord wrapped around the cylinder as shown to the right, is released. State all answers (aside from part b) in terms of

M,m

,

R

, and

g

.\ a. On the diagrams below, draw and label all the forces acting on the block and the pulley.\ b. Use the free body diagrams to write each of the following:\ i. The equation of translational motion for the block.\ ii. The analogous equation for the rotational motion of the pulley.\ c. Solve the equations in part

b

for the acceleration of the block.\ d. Determine the tension force in the segment of the cord attached to the block.\ e. Determine the angular momentum of the cylinder as a function of time.

A uniform solid cylinder of mass M and radius R is mounted on frictionless bearings about a fixed axis through the center of the cylinder. The moment of inertia of the cylinder about the axis is 1/2MR2. A block of mass m, suspended by a cord wrapped around the cylinder as shown to the right, is released. State all answers (aside from part b ) in terms of M,m, R, and g. a. On the diagrams below, draw and label all the forces acting on the block and the pulley. m b. Use the free body diagrams to write each of the following: i. The equation of translational motion for the block. ii. The analogous equation for the rotational motion of the pulley. c. Solve the equations in part b for the acceleration of the block. d. Determine the tension force in the segment of the cord attached to the block. e. Determine the angular momentum of the cylinder as a function of time