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A rigid body is free to rotate about a fixed axis. Can the body have nonzero angular acceleration even if the angular velocity of the body is (perhaps instantaneously) zero? What is the linear equivalent of this question? Give physical examples to illustrate both the angular and linear situations.

A rigid body is free to rotate about a fixed axis. Can the body have nonzero angular acceleration even if the angular velocity of the body is (perhaps instantaneously) zero? What is the linear equivalent of this question? Give physical examples to illustrate both the angular and linear situations.

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
6 years ago
Yes, a body can have nonzero angular acceleration even if the angular velocity of the body is instantaneously zero. This happens when the body changes the direction of the angular velocity, and at the instant the angular velocity in the final direction is equal in magnitude with the angular velocity in initial direction, the net angular velocity is zero.
However, the body will be at rest instantaneously, and as the magnitude of the final angular velocity will grow in magnitude relative to the initial angular velocity, the direction of the rotation of object will change.
Therefore at the instant when the object is about to reverse its direction of rotational motion, the object is experiencing an angular deceleration but there is no net angular velocity.
The similar thing happens with the velocity of the object, when the direction of velocity of object changes under the action of deceleration. There will be a moment when object experiences no velocity but it is still acted upon by the deceleration which would eventually reverse the direction of translational motion of the object.
For example, consider a wheel spinning counterclockwise and experiencing an angular deceleration. When the stops instantaneously the wheel is not rotating but the angular deceleration still acts on it, which changes the direction of rotation of wheel to clockwise.

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