Question

Two identical wheels, wheel 1 and wheel 2, initially at rest begin to rotate with constant angular accelerations α. After rotating through the same angular displacement, Δθ0, the angular velocity of wheel 1 is ω1 and the angular velocity of wheel 2 is ω2=3ω1. How does the angular acceleration of wheel 2, α2, compare to the angular acceleration of wheel 1, α1?a. a2 = a1b. a2 = a1/3c. a2 = 3a1d. a2 = 9a1

Answer 1

Answer:

a2 = 3a1

Explanation:

Detailed explanation and calculation is shown in the image below

Answer 2

Answer:

d. a2 = 9a1

Explanation:

We can apply the following equation of motion to calculate the angular acceleration:

$\omega^2 - \omega_0^2 = 2\alpha\theta$

Since both wheel starts from rest, their $\omega_0 = 0 rad/s$

$\omega^2 = 2\alpha\theta$

We can take the equation for the 1st wheel, divided by the equation by the 2nd wheel:

$\frac{\omega_1^2}{\omega_2^2} = \frac{2\alpha_1\theta_1}{2\alpha_2\theta_2}$

As they were rotating through the same angular displacement $\theta_1 = \theta_2$, these 2 cancel out

$\left(\frac{\omega_1}{\omega_2}\right)^2 = \frac{\alpha_1}{\alpha_2}$

$\left(\frac{1}{3}\right)^2 = \frac{\alpha_1}{\alpha_2}$

$\frac{1}{9} = \frac{\alpha_1}{\alpha_2}$

$\alpha_2 = 9\alpha_1$

So d is the correct answer