PHYS 211, Section 3 (Honors) – Review
Chapter 11: Rolling, Torque, and Angular Momentum
Rolling: If the object does not slip, its linear and angular motions are related by s = R and vcom = R,
and the kinetic energy is K = IP
2 = Icom
2 + mv2.
Problem solving: Be able to set up and solve problems with rolling objects using Newton's second law
and/or conservation of energy.
Angular momentum: For a particle moving in space, the angular momentum with respect to a point is
l = r x p .
For a system of particles, the total angular momentum L is the sum (as a vector) of all the l's. For an
object rotating around a fixed axis, the important component is the components along that axis, which is
L = I ,
where I is the rotational inertia around that axis.
Rotational inertia: For a small object of mass m a distance r away from the rotation axis, I = mr2.
Torque: For a particle or other object moving in space, the torque of a force F with respect to a point is
= r x F ,
where r is the radius vector from the reference point to the point where F is applied.
Angular form of second law: The net torque net = dL/dt is the time derivative of the angular
momentum.
Conservation of angular momentum: If the net (external) torque on a system is zero, its angular
momentum L is conserved, Li = Lf.
Precession of a gyroscope: We only saw a demonstration of precession – it will not be on tests.
Website by Luca Bombelli <bombelli"at"olemiss.edu>; Content of this page last modified on 8 nov 2009
