Question:

A student is performing an experiment to study the conservation of angular momentum. The student has a spinning bicycle wheel with an initial angular velocity of 5 rad/s. The student then extends his arms out, causing the moment of inertia of the system to decrease by a factor of 4. What will be the final angular velocity of the bicycle wheel?

Answer:

To solve this problem, we can use the conservation of angular momentum principle, which states that the initial angular momentum of a system will be equal to the final angular momentum of the system.

The equation for angular momentum is: [ L = I \times \omega ] Where: L = angular momentum I = moment of inertia ω = angular velocity

Initially, the moment of inertia and angular velocity are given as: [ I_1 = I_0 ] [ \omega_1 = 5 rad/s ]

Finally, the moment of inertia decreases by a factor of 4, so the new moment of inertia is $I_2 = \frac{1}{4} I_0$, and we're looking for the final angular velocity $\omega_2$.

According to the conservation of angular momentum: [ I_1 \times \omega_1 = I_2 \times \omega_2 ] [ I_1 \times \omega_1 = \frac{1}{4} I_0 \times \omega_2 ] [ \omega_2 = 4 \times \omega_1 ] [ \omega_2 = 4 \times 5 ] [ \omega_2 = 20 rad/s ]

Therefore, the final angular velocity of the bicycle wheel will be 20 rad/s.

The student can experience an increase in angular velocity when pulling their arms close (causing a decrease in moment of inertia) due to the conservation of angular momentum.