Indicate true or false in each of the following statements. a. The moment of inertia of a solid sphere can never be the same as that for a solid disk. b. The linear force equations have angular analogues. c. The moment of inertia of a sphere is greater if it is solid rather than hollow. d. A solid ball rolls down a slope faster than a solid disc. e. The axis of rotation does not affect the moment of inertia.

a) True

b) True

c) False

d) True

e) False

Explanation:

a) The moment of inertia of a solid sphere can never be the same as that for a solid disk. ... The moment of inertia of a sphere is greater if it is solid rather than hollow. A solid ballrolls down a slope faster than a soliddisc. The axis of rotation does not affect the moment of inertia.

b) Rotational Analogue of force in linear motion is torque. τ = r × F Force is necessary for a body to do translational motion. 

c) That means that the solid sphere has a lower moment of inertia. Since the mass of both are the same, the force of gravity on both is exactly the same. Since the hollow sphere has a greater moment of inertia, this force willcause it to accelerate more slowlythan the solid one.

 d) a solid object will always roll down the ramp faster than a hollow object of the same shape (sphere or cylinder)—regardless of their exact mass or diameter.

e)

The basic relationship between the moment of inertia and the angular acceleration is that the larger the moment of inertia, the smaller the angular acceleration.

the area between the graph and the t axis