Physics 430: Lecture 20 Non-Inertial Frames

A Useful Relation

• November 16, 2010

• It is important to realize that  need not be constant. In the case of a wheel whose rotation is accelerating, the magnitude changes with time. In the case of a wobbling top, the direction changes with time. In general t. The time rate of change of this is the angular acceleration (which need not be in the same direction as ).
• We also wish to point out a very useful relation
• You can see how this arises from the figure at right.
• There is, in fact, a corresponding relation for ANY vector
• in a rotating frame, which we will be using soon. If e is
• a unit vector fixed in a rotating body, then its rate of change
• as seen from the non-rotating frame is
• Note that one can add angular velocities just like linear velocities. If body 3 is rotating at angular velocity 32 relative to frame 2, and frame 2 is rotating at angular velocity 21 relative to frame 1, then body 3 is rotating relative to frame 1 at angular velocity

• P

• O

• r

•  = r sin

• 

• 