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Chapter 10 | Rotational Motion and Angular Momentum 419
momentum, or change in angular momentum of a system, or average torque or time during which the torque is exerted
in analyzing a situation involving torque and angular momentum. (S.P. 2.2)
• 4.D.3.2 The student is able to plan a data collection strategy designed to test the relationship between the change in
angular momentum of a system and the product of the average torque applied to the system and the time interval
during which the torque is exerted. (S.P. 4.1, 4.2)
• 5.E.1.1 The student is able to make qualitative predictions about the angular momentum of a system for a situation in
which there is no net external torque. (S.P. 6.4, 7.2)
• 5.E.1.2 The student is able to make calculations of quantities related to the angular momentum of a system when the
net external torque on the system is zero. (S.P. 2.1, 2.2)
• 5.E.2.1 The student is able to describe or calculate the angular momentum and rotational inertia of a system in terms of
the locations and velocities of objects that make up the system. Students are expected to do qualitative reasoning with compound objects. Students are expected to do calculations with a fixed set of extended objects and point masses. (S.P. 2.2)
Why does Earth keep on spinning? What started it spinning to begin with? And how does an ice skater manage to spin faster and faster simply by pulling her arms in? Why does she not have to exert a torque to spin faster? Questions like these have answers based in angular momentum, the rotational analog to linear momentum.
By now the pattern is clear—every rotational phenomenon has a direct translational analog. It seems quite reasonable, then, to define angular momentum as
(10.90) This equation is an analog to the definition of linear momentum as . Units for linear momentum are while
units for angular momentum are . As we would expect, an object that has a large moment of inertia , such as Earth,
has a very large angular momentum. An object that has a large angular velocity , such as a centrifuge, also has a rather large angular momentum.
Making Connections
Angular momentum is completely analogous to linear momentum, first presented in Uniform Circular Motion and Gravitation. It has the same implications in terms of carrying rotation forward, and it is conserved when the net external torque is zero. Angular momentum, like linear momentum, is also a property of the atoms and subatomic particles.
Example 10.11 Calculating Angular Momentum of the Earth
Strategy
No information is given in the statement of the problem; so we must look up pertinent data before we can calculate . First, according to Figure 10.12, the formula for the moment of inertia of a sphere is

exactly one revolution per day, but we must covert to radians per second to do the calculation in SI units. Solution
Substituting known information into the expression for and converting to radians per second gives
(10.93)
(10.94)
so that

(10.92) Earth's mass is and its radius is . The Earth's angular velocity is, of course,
(10.91)

Substituting rad for rev and for 1 day gives