Rotational and translational motion of a ruler on a pivot

In summary, a student exerts a downward force on the right end of a ruler attached to a frictionless pivot point. The force applied is smaller than the weight of the ruler, causing it to spin clockwise and then counter-clockwise back to its resting position. However, the motion of the ruler's center of mass will not change as long as the pivot point remains frictionless. Even if the force applied is small, the ruler will continue spinning.
  • #1
paulsberardi
8
0

Homework Statement


A ruler is attached to the top of a pole bound by its center (pivot point of the ruler is at its center). A student briefly exerts a downward force on the right end of the ruler. The magnitude of the force exerted by the student is less than the weight of the ruler. Assume that pivot point is frictionless.


Homework Equations


After the student stops pushing the ruler, will it continue spinning or come to a stop?
Does the motion of the ruler's center of mass ever change?

The Attempt at a Solution


I am assuming the ruler will spin forever if the pivot point is frictionless, but I wasn't sure because the force applied on it was less than its weight. That had me thinking of the possibility that the ruler's motion may change direction and it will be restored to its original position.
 
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  • #2
I believe if the force is less than the weight of the ruler then the ruler wouldn't spin. It would rotate clockwise then counter-clockwise back to the resting position.
 
  • #3
You are right that if there is no friction the ruler will continue spinning.

As for the second part, remember that there is a difference between the "ruler's motion" and the "motion of the ruler's center of mass".

Does this help?
 
  • #4
@longball, the force exerted on the ruler will cause the ruler to spin even if it is much lighter than the ruler's weight. If the force was greater than the ruler's weight then the ruler could be "broken off" the pivot point. I think the point of the question was just to assume that the applied force was small compared to the weight of the ruler so that the ruler remains fixed at the pivot point.
 
  • #5
Bacat said:
You are right that if there is no friction the ruler will continue spinning.

As for the second part, remember that there is a difference between the "ruler's motion" and the "motion of the ruler's center of mass".

Does this help?

Yes, so how will the motion of the ruler's center of mass change? And it doesn't matter how small the magnitude of the force applied is, it could still spin forever?
 

FAQ: Rotational and translational motion of a ruler on a pivot

What is rotational and translational motion?

Rotational motion is the movement of an object around an axis or pivot point. Translational motion is the movement of an object in a straight line. In the case of a ruler on a pivot, the rotational motion would be the rotation of the ruler around the pivot point, while the translational motion would be the linear movement of the ruler along the pivot.

How is rotational and translational motion measured?

Rotational motion is commonly measured in terms of angular velocity, which is the rate at which an object rotates around an axis. Translational motion is measured in terms of linear velocity, which is the rate at which an object moves in a straight line.

What is the relationship between rotational and translational motion?

Rotational and translational motion are related through the concept of torque. Torque is the force that causes rotational motion, and it is directly proportional to the distance between the axis of rotation and the point where the force is applied. As the torque increases, the rotational motion increases, and the translational motion also increases.

How does the pivot point affect the motion of a ruler?

The pivot point, or axis of rotation, is a fixed point around which the ruler rotates. The position of the pivot point can greatly affect the motion of the ruler. If the pivot point is close to one end of the ruler, the rotational motion will be greater, while the translational motion will be smaller. If the pivot point is in the middle of the ruler, the rotational and translational motions will be more balanced.

What factors can affect the rotational and translational motion of a ruler on a pivot?

The rotational and translational motion of a ruler on a pivot can be affected by factors such as the length and mass of the ruler, the position of the pivot point, and the amount of force applied to the ruler. Friction between the ruler and the pivot point can also affect the motion.

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