# Characteristics of a rigid body.

1. Jun 25, 2013

### andyrk

Why is the angular velocity and angular acceleration(if the rigid body has some) same for all points on a rigid body?

2. Jun 25, 2013

### CWatters

What would happen if the front and back of a car had different velocity?

3. Jun 25, 2013

### haruspex

Take an angle fixed by three points A, B, C within the body. As the body rotates, the angle ABC must be preserved. So AB and BC must rotate by the same angle. Differentiating, deduce that the angular velocities and accelerations must also be the same.

4. Jun 25, 2013

### andyrk

But this gets that angular velocity of AB=angular velocity of BC
How does this get that angular velocity of A,B,C are equal?

5. Jun 25, 2013

### SteamKing

Staff Emeritus
Hint: look up the definition of 'rigid'.

6. Jun 25, 2013

### CWatters

The points are arbitrary. So the centre of rotation can be B. That means the angular velocity of A is the same as the angular velocity of AB...

Angular velocity of A = Angular velocity of AB = Angular velocity of CB = Angular velocity of C

It's why I asked the question above. If two points on a body have different velocity (angular or linear) then those points must get closer together or further apart which would imply it's not a rigid body.