Kevin Zhou — Advanced Mechanics IV Problem 3 · Kevin Zhou #M8.3
Physics · mechanics
Problem
Problem 3 (KK 7.1). A thin hoop of mass M and radius R rolls without slipping about the z-axis.
It is supported by an axle of length R through its center, as shown.
The axle circles around the z-axis with angular speed Ω, so that the bottom point of the wheel
traces out a circle of radius R. Let O be the pivot point of the rod, i.e. the point where the rod
meets the z-axis.
(a) Find the instantaneous angular velocityω of the hoop. (Before moving forward, you’ll want
to be totally sure you have this part right. Sometimes, students get confused on it because
they imagine a symmetric pair of hoops instead. However, if you actually had a pair, the
setup wouldn’t even make sense. Why not?)
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(b) As the motion continues, the angular velocity vector rotates in a circle. Find the precession
rate Ω of this system.
(c) Find the instantaneous angular momentum L of the hoop, about the point O.