10.8 - Angular momentum of a particle in circular motion
The concepts of linear momentum and conservation of linear momentum prove very
useful in understanding phenomena such as collisions. Angular momentum is the
rotational analog of linear momentum, and it too proves quite useful in certain settings.
For instance, we can use the concept of angular momentum to analyze an ice skater’s
graceful spins.
In this section, we focus on the angular momentum of a single particle revolving in a
circle. Angular momentum is always calculated using a point called the origin. With
circular motion, the simple and intuitive choice for the origin is the center of the circle,
and that is the point we will use here. The letter L represents angular momentum.
As with linear momentum, angular momentum is proportional to mass and velocity.
However, with rotational motion, the distance of the particle from the origin must be
taken into account, as well. With circular motion, the amount of angular momentum
equals the product of mass, speed and the radius of the circle: mvr. Another way to
state the same thing is to say that the amount of angular momentum equals the linear
momentum mv times the radius r.
Like linear momentum, angular momentum is a vector. When the motion is
counterclockwise, by convention, the vector is positive. The angular momentum of
clockwise motion is negative. The units for angular momentum are kilogram-meter^2 per
second (kg·m^2 /s).Angular momentum of a particle
Proportional to mass, speed, and
distance from originL = mvr
L = angular momentum
m= mass
v = speed
r = distance from origin (radius)
Counterclockwise +, clockwise í
Units: kg·m^2 /s
How much angular momentum
does the engine have?
L = ímvr
L = í(0.15 kg)(1.1 m/s)(0.50 m)
L = í0.083 kg·m^2 /s
(^196) Copyright 2007 Kinetic Books Co. Chapter 10