Question

An 86.0 kg solid sphere of radius 0.450m start from rest and turns with constant angular acceleration around the axle rod, rotating through 12.6 rad in 3.50 s

a. calculate its angular velocity at this time.

b. calculate its kinetic energy at the end of this process

Answer 1

Given is:-

Mass of the sphere m=86kg

radius of the sphere r=0.450m

Rotating 12.6 rad in 3.50 seconds.

Now,

Part-a

using second equation of motion we get

by plugging all the values we get

which gives us angular acceleration which is

Thus the angular speed at this instant is

which gives

Part-b

The moment of inertia of a solid sphere around its axle rod is given by

by plugging all the values we get

which gives

Therefore its kinetic energy at the end of this process is

again by plugging all the values we get