# Rotating ruler

## 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

## Answers and Replies

kuruman
Science Advisor
Homework Helper
Gold Member
You are correct on 1.

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

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

kuruman
Science Advisor
Homework Helper
Gold Member
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
Mentor
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.)