Question

A bowling ball of mass 7.23 kg and radius 10.3 cm rolls without slipping down a lane at 2.90 m/s .

Calculate its total kinetic energy.

Express your answer using three significant figures and include the appropriate units

Answer 1

KE(total) = KE(t) + KE(r)
= (mv² / 2) + (I?² / 2)

Moment of inertia, I, for a uniform solid sphere is:

I = 2mr² / 5

So the last equation becomes:

KE(total) = (mv² / 2) + (mr²?² / 5)

The angular speed, ?, is:
  There are two types of kinetic energy here: translational and rotational. The total KE is the sum of these two types of KE:

? = v / r
= 2.90m/s / .103m
= 28.15rad/s

T.E= [(7.23kg)(2.90m/s)² / 2] + [(7.23kg)(0.103m)²(28.15rad/s)² / 5]
= 30.41 J

Hope it will help you.

Please rate the answer.