Chapter 11, Problem 1OQ

To determine

The increase in rotational kinetic energy.

Answer to Problem 1OQ

Option (b) the rotational kinetic energy increases by factor $2$.

Explanation of Solution

Write the expression for angular momentum of an object.

  $L=I\omega$                                                                                                           (I)

Here, $L$ angular momentum of the object measured with respect to the axis of rotation for object, $I$ momentum of inertia with respect to the axis of rotation for object and $\omega$ is the angular velocity of rotation.

Write the expression for rotational kinetic energy of an object.

  $K.E=\frac{1}{2}I{\omega }^2$                                                                                                 (II)

Here, $K.E$ is rotational kinetic energy.

Conclusion:

Consider an ice skater is behaves like isolated system.

For conservative angular momentum when moment of inertia decreases by factor $2$ then angular velocity will increases by factor $2$

Substitute $\frac{I}{2}$ in place of $I$ and $2\omega$ in place of $\omega$ in equation (II).

  $\begin{array}{c}K.E=\frac{1}{2}\left(\frac{I}{2}\right){\left(2\omega \right)}^2\\ =I{\omega }^2\end{array}$

From the above expression clearly shows the rotational kinetic energy becomes double.

Thus, the rotational kinetic energy increases by factor $2$ so option (b) is correct.

When M.O.I decreases by four times than the rotational kinetic energy increases by factor $4$ so option (a) is incorrect.

When moment of inertia decreases than the rotational kinetic energy can’t be constant so option (c) is incorrect.

When moment of inertia decreases than the rotational kinetic energy can’t decreases so option (d) is incorrect.

When moment of inertia decreases than the rotational kinetic energy can’t decreases so option (e) is incorrect.