Motion of the centre of mass of a stick

[ppy]

A thin stick of length L is balanced vertically on frictionless ice. What happens to the motion of the centre of mass if it gets a big push above the centre of mass of the stick? Does the centre of mass move? If so how do you work it out?

This is more of an extra question I thought of when doing a homework problem

Explanations would be great thanks :)

We are assuming the centre of mass of the stick is at L/2

 

[ehild]

A thin stick of length L is balanced vertically on frictionless ice. What happens to the motion of the centre of mass if it gets a big push above the centre of mass of the stick? Does the centre of mass move? If so how do you work it out?

This is more of an extra question I thought of when doing a homework problem

Explanations would be great thanks :)

We are assuming the centre of mass of the stick is at L/2

With the "push", do you mean an impulse FΔt? Getting an impulse , what happens to the momentum of the stick? And momentum of the whole stick is related to the velocity of the CM - how?


whild

 

[ppy]

yes I meant if you apply a force to the stick above its centre of mass. If the stick has a force applied at this point does it still rotate about its centre of mass and will the centre of mass still fall vertically?

Also another question, if a stick is placed vertically on frictionless ice as above and due to a slight disturbance(a gentle wind) it loses balance and begins to fall under gravity.

now I know the centre of mass of the stick falls vertically downwards but why? 2 questions

 

[ehild]

yes I meant if you apply a force to the stick above its centre of mass. If the stick has a force applied at this point does it still rotate about its centre of mass and will the centre of mass still fall vertically?

Also another question, if a stick is placed vertically on frictionless ice as above and due to a slight disturbance(a gentle wind) it loses balance and begins to fall under gravity.

now I know the centre of mass of the stick falls vertically downwards but why? 2 questions

If you push it horizontally, you give the stick a horizontal momentum. The CM will fall, and at the same time, it moves also horizontally, like a projectile. During its fall, it is subjected to gravity and the normal force from the ground. Their resultant determine the vertical acceleration of the CM.

The initial push above the CM also gives it angular momentum. So the stick starts also rotate about the CM.
The normal force from the ground has a torque with respect to the CM, and it determines the angular acceleration of rotation.

In the other case, when there is only a slight disturbance, but the stick loses balance, the initial horizontal velocity of the CM can be taken zero. The stick is subjected to gravity and the normal force, both vertical, so the CM will move with acceleration vertically.


ehild

 

[haruspex]

Here's a challenge question: for what position/magnitude of push will the stick become airborne?