Question

Consider a uniform solid sphere of radius R and mass M rolling without slipping. Which form of its kinetic energy is larger, translational or rotational?A. Its translational kinetic energy is larger than its rotational kinetic energy.B. Its rotational kinetic energy is larger than its translational kinetic energy.C. You need to know the speed of the sphere to tell.

Answer 1

Answer:

A. Its translational kinetic energy is larger than its rotational kinetic energy.

Explanation:

Given that

Radius = R

Mass = M

We know that mass moment of inertia for the solid sphere

$I=\dfrac{2}{5}MR^2$

Lets take angular speed =ω

Linear speed =V

Condition for pure rolling , V= ω R

Rotation energy ,RE

$RE=\dfrac{1}{2}I\omega^2$

$RE=\dfrac{1}{2}\times \dfrac{2}{5}MR^2\times \omega^2$

$RE=\dfrac{1}{2}\times \dfrac{2}{5}MR^2\times \omega^2$

$RE=\dfrac{1}{5}\times MR^2\times \omega^2$

$RE=\dfrac{1}{5}\times MV^2$

RE= 0.2  MV²

The transnational kinetic energy TE

$TE=\dfrac{1}{2}MV^2$

TE= 0.5 MV²

From above we can say that transnational energy is more than rotational energy.

Therefore the answer is A.