Chapter 9, Problem 95A

To determine

To Explain: Whether one would expect the student and stool to turn and if yes, then in which direction.

Explanation of Solution

Introduction:

Yes, student with stool will rotate. It is all because of principle of angular momentum conservation.

Here, as it is given that student is holding the wheel of the cycle and also the stool is frictionless, so there is no external torque is acting on it. According to principle of angular momentum conservation:

Initial angular momentum of student +cycle wheel = final angular momentum of student +cycle wheel

Since initially student and wheel both were at rest, so the initial angular momentum of both must zero.

Final angular momentum of student + cycle wheel = 0

Final angular momentum of student + Final angular momentum of wheel = 0

Final angular momentum of student = - (Final angular momentum of wheel)

  $\begin{array}{l}{I}_1{\omega }_1=-I_2{\omega }_2\\ {\omega }_1=-\frac{I_2{\omega }_2}{I_1}\end{array}$

Conclusion:

Hence, final angular momentum of student is equal in magnitude of angular momentum of wheel. Also it is opposite direction to that of wheel also.