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Chapter 10 | Rotational Motion and Angular Momentum 431
Figure 10.31 As seen in figure (a), the forces on a spinning gyroscope are its weight and the supporting force from the stand. These forces create a horizontal torque on the gyroscope, which create a change in angular momentum that is also horizontal. In figure (b), and add to
produce a new angular momentum with the same magnitude, but different direction, so that the gyroscope precesses in the direction shown instead of falling over.
Glossary
angular acceleration: the rate of change of angular velocity with time
angular momentum: the product of moment of inertia and angular velocity
change in angular velocity: the difference between final and initial values of angular velocity
kinematics of rotational motion: describes the relationships among rotation angle, angular velocity, angular acceleration, and time
law of conservation of angular momentum: angular momentum is conserved, i.e., the initial angular momentum is equal to the final angular momentum when no external torque is applied to the system
moment of inertia: mass times the square of perpendicular distance from the rotation axis; for a point mass, it is and, because any object can be built up from a collection of point masses, this relationship is the basis for all other
moments of inertia
right-hand rule: direction of angular velocity ω and angular momentum L in which the thumb of your right hand points when you curl your fingers in the direction of the disk's rotation
rotational inertia: resistance to change of rotation. The more rotational inertia an object has, the harder it is to rotate rotational kinetic energy: the kinetic energy due to the rotation of an object. This is part of its total kinetic energy tangential acceleration: the acceleration in a direction tangent to the circle at the point of interest in circular motion torque: the turning effectiveness of a force
work-energy theorem: if one or more external forces act upon a rigid object, causing its kinetic energy to change from to , then the work done by the net force is equal to the change in kinetic energy
Check Your Understanding
Rotational kinetic energy is associated with angular momentum? Does that mean that rotational kinetic energy is a vector?
Solution
No, energy is always a scalar whether motion is involved or not. No form of energy has a direction in space and you can see that rotational kinetic energy does not depend on the direction of motion just as linear kinetic energy is independent of the direction of motion.