Question

Two identical masses are hung from two different flywheels that are initially stationary. Flywheel B is a uniform disk. Flywheel A has less mass than flywheel B, and its mass is distributed in a uniform ring that is attached to the rotational axis by spokes of negligible mass.
The identical masses are released and allowed to drop from
the same height to the floor. Which of the following statements is correct?
a) The angular accelerations of the two flywheels are equal.
b) The angular acceleration of flywheel A is greater than flywheel B.
c) The angular acceleration of flywheel A is smaller than flywheel B.
d) The angular momentum of the two flywheels will be the same.
e) The kinetic energy of the two flywheels will be the same.

Answer 1

Answer:

Option C

The angular acceleration of flywheel A is smaller than flywheel B.

Explanation:

Flywheel B

T = mgr   where m is mass, g is acceleration due to gravity, r is the radius

$0.5 mr^{2}\times a_B​​​​​​=mgr$

$a_B​​​​​​= \frac {2g}{r}$ where $a_B$ is angular acceleration of Flywheel B

Flywheel A

$mr^{2}\times a_A​​​​​​= mgr$

$a_A=\frac {g}{r}$ where $a_A$ is angular acceleration of Flywheel A

so, $a_A​​​​​​$

Therefore, the angular acceleration of flywheel A is smaller than flywheel B.