A wheel with a 0.10-m radius is rotating at 35 rev/s. It then slows uniformly to 15 rev/s over a 3.0-s interval. What is the angular acceleration of a point on the wheel?
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The angular acceleration is the change in angular velocity divided by the time it takes for that change to occur.
First, we need to convert the revolutions per second to radians per second. There are 2π radians in one revolution, so:
Initial angular velocity = 35 rev/s * 2π rad/rev = 70π rad/s
Final angular velocity = 15 rev/s * 2π rad/rev = 30π rad/s
The change in angular velocity is the final angular velocity minus the initial angular velocity:
Change in angular velocity = 30π rad/s - 70π rad/s = -40π rad/s
The time it takes for this change to occur is given as 3.0 s.
So, the angular acceleration is:
Angular acceleration = Change in angular velocity / time = -40π rad/s / 3.0 s = -40π/3 rad/s².
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