5.docx - rigid body whose angular velocity changes has an angular acceleration When you pedal your bicycle harder to make the wheels turn faster or

5.docx - rigid body whose angular velocity changes has an...

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rigid body whose angular velocity changes has an angular acceleration. When you pedal your bicycle harder to make the wheels turn faster or apply the brakes to bring the wheels to a stop, you’re giving the wheels an angular acceleration. If v 1 z and v 2 z are the instantaneous angular velocities at times t 1 and t 2 , we define the average angular acceleration a [email protected] z over the interval ∆ t = t 2 - t 1 as the change in angular velocity divided by ∆ t ( Fig. 9.6 ): a [email protected] z = v 2 z - v 1 z = ∆v z (9.4) t 2 - t 1 t The instantaneous angular acceleration a z is the limit of a [email protected] z as ∆ t S 0: eration of a rotating rigid body. The average angular acceleration is the change in angular velocity divided by the time interval: a av-z = v 2 z - v 1 z = ∆v z The instantaneous angular ∆v z acceleration of a rigid body a z = lim rotating around the z -axis ... t S 0 t ... equals the limit of the body’s average angular acceleration as the time interval approaches zero ...
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