Rotational Motion of a Mass on a Table: Solutions

[benf.stokes]

Homework Statement

We have a rule of mass m and length l lying on a table without friction.

We give a boost I to the rule at a distance d from the center of mass so that it now has a rotation and a translation.

1) The rule rotates about which point?

2) Determine the velocity, vm, of the center of mass.

3) Determine the angular velocity, w, of the ruler.

4)What should be the distance d so that the instantaneous displacement ds of the oposite side of the ruler be a minimum?

Homework Equations

w=v*r
I= Variation momentum

The Attempt at a Solution

I think the answer to 1 is that it rotates about it center of mass but I don't have a clue about the other ones

 

[kuruman]

You are correct on 1.

Another word for "boost I" is "impulse I". Does this mean something to you?

 

[benf.stokes]

Yes impulse is the change in momentum but how do I know the direction of the resulting velocity?

 

[kuruman]

Put a ruler on a table and give it a sharp flick with your finger. That's the impulse. In what direction is the impulse? In what direction does the ruler move?

 

[Doc Al]

I think the answer to 1 is that it rotates about it center of mass but I don't have a clue about the other ones

I suspect they are asking about the instantaneous axis of rotation, which won't be the center of mass. (Since it's also translating.)