Characteristics of a rigid body.

[andyrk]

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

 

[CWatters]

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

 

[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.

 

[andyrk]

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.

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?

 

[SteamKing]

Hint: look up the definition of 'rigid'.

 

[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.