Question

A wheel, which is at rest gains an angular velocity of 12.6 rad/s when it rotates through 10 revolutions. Its angular acceleration is closet to

A) 6.80 rad/s
B) 2.49 rad/s
C) 1.26 rad/s
D) 8.40 rad/s

Answer 1

The angular acceleration of the wheel is 15.87 rad/s², which is not one of the given options.

Step-by-step explanation:

To find the angular acceleration of the wheel, we can use the formula:

angular acceleration (α) = (change in angular velocity (Δω))/(time taken (t))

Given that the wheel gains an angular velocity of 12.6 rad/s when it rotates through 10 revolutions, we can calculate the change in angular velocity by converting the revolutions to radians:

change in angular velocity (Δω) = (12.6 rad/s) - 0 rad/s = 12.6 rad/s

The time taken (t) can be calculated using the formula:

time taken (t) = (number of revolutions)/(angular velocity)

t = 10 rev / (12.6 rad/s) = 0.7937 s

Substituting the values into the formula for angular acceleration:

angular acceleration (α) = (12.6 rad/s) / (0.7937 s) = 15.87 rad/s²

Therefore, the closest value to the angular acceleration is 15.87 rad/s², which is not one of the given options.