# Does rotation of rigid body need a couple or only 1 force is sufficien

1. Dec 23, 2013

### koolraj09

Hi all,

Suppose we go in space where no gravity and friction exists. If there is a bar, in say - horizontal plane and we apply a force at one end of the bar, in this plane and perpendicular to the bar. Will that bar rotate and translate or it will only undergo pure translational motion without rotation?
In other words is it sufficient to apply a single force and cause a body to rotate? Or do we need to apply a couple/moment to make the body rotate.

2. Dec 23, 2013

### mikeph

It will rotate and translate.

3. Dec 23, 2013

### koolraj09

Can you please give me an elaborate explanation as why this is true?

4. Dec 23, 2013

### mikeph

If the force vector is F and the position of the point of application of that force is r (measured from the body's centre of mass), then the torque is r cross F. If you apply a force on the bar in the way you describe, r cross F is nonzero so the torque is nonzero, which means the object will gain angular momentum, i.e. begin to rotate.

5. Dec 23, 2013

### koolraj09

Can only one single force provide this rotation (as well as translation) or we need some other force to produce this rotation?

6. Dec 23, 2013

### mikeph

Yes, a single force can provide this, as long as r cross F is not zero.

7. Jan 2, 2014

### koolraj09

Thanks guys. The explanation is obviously right. But I am still not convinced.
Can you suggest me some experiment in which I will be able to confirm/demonstrate this fact - the fact that a rigid body can rotate when only a single force acts on the whole body with no counter/opposing force present?

8. Jan 3, 2014

### Tanya Sharma

Have you ever played billiards/snooker/pool ? In the game if you hit the ball right in the middle ,it would simply move forward .But if you hit it above or below the center of the ball ,it would rotate as well as translate forward .

In real life friction is present ,but even in an ideal case ,if we assume friction to be absent , a force above or below the center of the ball would cause the ball to rotate.

9. Jan 3, 2014

### koolraj09

Thanks Tanya! Still are there any other examples which could prove this fact?

In this example - What 'r' would we take to calculate torque (=rXF)? About which point would the body rotate?

10. Jan 3, 2014

### Staff: Mentor

Have you ever kicked a football? Kick it off center and it goes flying and rotates.

It's always convenient to use the center of mass as your reference in calculating 'r'--take r to be the distance from the center of mass. The motion can be consider to be a combination of translation and rotation about the center of mass.

11. Jan 3, 2014

### Tanya Sharma

Place a light wooden scale on a sufficiently smooth table .Just flick one end of it with your fingers (i.e give it a sharp impulse ) .You will find the scale rotating as well as moving forward.

'r' is the distance between the point of application of force and the center of mass of the object.

The body rotates about its center of mass .

Please note that if a body is unconstrained (i.e free to move ) and an off center force/impulse is applied ,then the body moves such that the center of mass moves in a straight line and the body rotates about the CM .

Hope this helps