Question

A vertical wheel with a diameter of 50 cm starts from rest and rotates with a constant angular acceleration of 4 rad/s^2 around a fixed axis through its center counterclockwise. What is the angular velocity after 3 seconds?

a) 12 rad/s
b) 24 rad/s
c) 36 rad/s
d) 48 rad/s

Answer 1

The angular velocity of a wheel with a constant angular acceleration of 4 rad/s² after 3 seconds is 12 rad/s, as calculated by the equation ω = αt.

Step-by-step explanation:

The angular velocity (ω) of a wheel after some time (t) when it starts from rest can be calculated using the equation ω = αt, where α is the angular acceleration. Given that the angular acceleration is 4 rad/s² and the time is 3 seconds, we can calculate the angular velocity after 3 seconds by multiplying the angular acceleration by the time.

ω = αt = (4 rad/s²)(3 s) = 12 rad/s

Therefore, the angular velocity of the wheel after 3 seconds is 12 rad/s, which corresponds to option (a).

Answer 2

The angular velocity of the wheel after 3 seconds is 12 rad/s. Therefore, the correct answer is:

a) 12 rad/s

To find the angular velocity of the wheel after 3 seconds, given that it starts from rest and rotates with a constant angular acceleration, we can use the formula for angular velocity in rotational motion:

`\[ \omega = \omega_0 + \alpha t \]`

Where:

`\( \omega \)` is the final angular velocity.

`\( \omega_0 \)` is the initial angular velocity.

`\( \alpha \)` is the angular acceleration.

`\( t \)` is the time.

Given in the problem:

- The wheel starts from rest, so
`\( \omega_0 = 0 \, \text{rad/s} \).`

- The angular acceleration
`$\alpha=4 \mathrm{rad} / \mathrm{s}^2$`

- The time
`\( t = 3 \, \text{s} \).`

Now, substituting these values into the formula, we get:

`\[ \omega = 0 + 4 * 3 \]`

= 12 rad/s