A ruler is initially at rest when a student briefly exerts a downward force on the right end. The magnitude of the force exerted by the student is less than the weight of the ruler. Assume that the pivot point in the center of the ruler is frictionless. Answer the following questions based on this description.

Question

While the hand is pushing, but before the ruler begins to move, what is the:
tangential acceleration?
centripetal acceleration?
angular acceleration?

At the instant the hand has stopped pushing, what is the:
tangential accleration?
centripetal acceleration?
angular acceleration?

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Assuming that the ruler's circular motion is drawn on a page's plane: for the first situation, since a force has been exerted downward, there is a torque going into the page. Therefore, tangential acceleration should be perpendicular to the ruler and in the plane of the page. Centripetal would be along the ruler and toward the center, and angular acceleration would be the same as tangential?
For the second situation is it the same as the first? I don't know if the first situation's answer is zero for all since it has not yet moved and acceleration is the time derivative of change in position.

Any help is appreciated, thanks

Answer 1

There is no centripetal acceleration before the motion starts.
Ac = V^2/R = omega^2 * R
V = omega * R = 0 at start so Ac = 0

There is however an angular acceleration
alpha = Torque/moment of inertia
The tangential acceleration = alpha * R
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When you stop pushing:
The angular acceleration and tangential acceleration become zero because there is no force or moment.
HOWEVER you still have angular velocity and tangential velocity
V = omega * R
SO
You still have centripetal acceleration
Ac = omega^2 * R = V^2/R

Answer 2

Thank you!