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Keith_Richards [23]
4 years ago
14

Two identical wheels, wheel 1 and wheel 2, initially at rest begin to rotate with constant angular accelerations α. After rotati

ng 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

Physics
2 answers:
Thepotemich [5.8K]4 years ago
6 0

Answer:

a2 = 3a1

Explanation:

Detailed explanation and calculation is shown in the image below

Georgia [21]4 years ago
5 0

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

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