Question

A wheel accelerates from rest with 4 rad/s². How many revolutions are experienced in 8 seconds?

Answer 1

The wheel experiences approximately 5.09 revolutions in 8 seconds.

Step-by-step explanation:

To calculate the number of revolutions, we need to find the final angular velocity of the wheel.

Given:

• Initial angular velocity (ωi) = 0 rad/s (as it starts from rest)
• Angular acceleration (α) = 4 rad/s²
• Time (t) = 8 s

Using the formula:

Final angular velocity (ωf) = ωi + αt

Plugging in the values:

ωf = 0 + (4 rad/s²)(8 s)

ωf = 32 rad/s

Now, we can calculate the number of revolutions:

• 1 revolution = 2π radians
• Number of revolutions = final angular displacement / (2π)

Using the formula:

Number of revolutions = (ωf) / (2π)

Plugging in the value:

Number of revolutions = (32 rad/s) / (2π)

Number of revolutions ≈ 5.09 revolutions