Question

A wheel starts from rest with uniform angular acceleration. In 3 seconds, its angular displacement is θ. In the 3rd second, its angular displacement is:

a. 2θ
b. 3θ
c. 4θ
d. θ/3

Answer 1

The angular displacement of the wheel in the third second is 3θ.

Step-by-step explanation:

To find the angular displacement of the wheel in the third second, we need to first find its angular velocity at the end of the second second. Using the formula:

angular velocity (ω) = initial angular velocity + (angular acceleration x time)

angular velocity (ω) = 0 + (angular acceleration x 2)

angular velocity (ω) = 2θ

Now, to find the angular displacement in the third second, we use the formula:

angular displacement (θ) = initial angular displacement + (angular velocity x time)

angular displacement (θ) = θ + (2θ x 1)

angular displacement (θ) = 3θ

Therefore, the angular displacement in the third second is 3θ.

So, the correct answer is b. 3θ.