a body is free to rotate about a fixed axis. can the body have nonzero angular acceleration?

Question

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? give an example to illustrate your answer

Answer 1

Say you are spinning a basketball on your finger. It is traveling clockwise. If you start to push it counter-clockwise, it will eventually slow down in the clockwise direction and start moving counter-clockwise (assuming it doesn't fall off you finger, we'll assume it doesn't for the sake of example).

When something is spinning one way, then starts spinning the other way, it had to at some point be perfectly still. At the time it switches over, the instantaneous velocity is zero, but it is still accelerating in the counter-clockwise direction (i.e. it will spin counter-clockwise without any further outside forces applied).

Hard to show without a diagram or something. Hopefully I explained it well enough.

Answer 2

First of all, this is the same exact case if you consider linear displacement/velocity/acceleration.

So just like how it is possible for a body to have zero linear accleration if it is free to move about (without any additional forces), it is also possible for a rotating object to have zero angular accleration if it is free to move about a fixed axis.

Constant velocity implies that the accleration is zero.
Constant linear velocity implies that the linear accleration is zero.
Constant angular velocity implies that the angular acceleration is zero.

So, if I have the body rotating at a constant angular velocity (like 5 rounds per minute or something), then the angular accleration is zero.

If the angular velocity is not zero (which is implied by the details of your question, because instantaneously zero mean that it was non-zero before, and non-zero after, which meand that the angular velocity is changing) then of course the angular acceleration is nonzero.

Remember, acceleration is DEFINED to be the timed rate of change of velocity. The only way you are going to get zero acceleration is...when velocity is not changing with time. So if the acceleration is changing with time, the acceleration is nonzero.

Answer 3

Steve S has given you an excellent example and correct answer.

For angular acceleration a torque (Moment of couple) is always necessary.

Torque is the product of moment of inertia and angular acceleration.

When ever there is a net (unbalanced) torque there will be angular acceleration.

If an object is under the condition of two equal but opposite torque the net torque is zero. The object can either be at uniform rotational motion or with zero angular velocity.

When one of the torques is removed, the other one begins to act at once. The angular acceleration (a = Torque / moment of inertia) - a non zero value- begins to act even though the angular speed at that instant is zero.

In the case of linear speeds, (like freely bodies under the action of gravitational acceleration, the bob oscillating in a simple pendulum, a body at rest on certain height from ground) the speed is zero but there is an acceleration at the beginning and after the motion.

Similarly in the case of rotational motion, when ever there is a torque, the angular acceleration will always be there even when there is zero angular speed.

A roller on an inclined road is rest by some obstacle. When the obstacle is removed, torque begins to act and the roller rotates down the inclined plane due to angular acceleration (torque)
At start the angular speed is zero; but the angular acceleration is not zero. If the latter is zero then it will not rotate at all.

A disc with its plane in horizontal position is suspended in a string. The string is twisted for some time and it is left free.
At the start it is at rest. Then it begins to rotate with angular acceleration, at the start its speed is zero, but not the angular acceleration.

A ball is made to roll up and down inside a hemi spherical surface. When the ball is in its height position its angular speed is zero, but its angular acceleration is not zero.

When a car is at rest on a level road, the angular speeds of the wheels are zero. When the car is accelerated, all the wheel begins to rotate because of angular acceleration even though at start the angular speed is zero.

When a fan is switched on, initially the angular speed is zero but not the angular acceleration.

In a see-saw, when the plank is at rest, the angular acceleration is not zero.

In general any object cannot start its rotation unless there is an angular acceleration.

Answer 4

According to SCIENCE anyway, IF IT CAN'T BE PROVEN, IT AIN'T SO!!