A cyclist starts from rest and pedals so that the wheels make 7.7 revolutions in the first 5.1 s. What is the angular acceleration of the wheels (assumed constant)?
To find the angular acceleration of the wheels, we need to use the formula:
Angular acceleration (α) = (Change in angular velocity) / (Change in time)
In this case, the cyclist starts from rest, so the initial angular velocity (ω1) is 0. The final angular velocity (ω2) can be calculated using the formula:
Angular velocity (ω) = (2π * Number of revolutions) / (Time)
Given that the wheels make 7.7 revolutions in the first 5.1 seconds, we can substitute these values into the formula:
ω2 = (2π * 7.7) / 5.1
Next, we find the change in angular velocity by subtracting the initial angular velocity from the final angular velocity:
Change in angular velocity = ω2 - ω1
Since ω1 = 0, the change in angular velocity is simply ω2:
Change in angular velocity = ω2
Finally, we substitute the values into the formula for angular acceleration:
Angular acceleration (α) = Change in angular velocity / Change in time
Thus,
Angular acceleration (α) = ω2 / 5.1
By calculating ω2 and dividing it by the given time of 5.1 seconds, we can find the angular acceleration of the wheels.