Q:  I'm trying to explain to my 14-year old daughter the difference between inertia and momentum; can you give any good examples?  Doug, London, England.

The catcher will soon feel the ball's inertia effect as it comes to a stinging stop in his mitt.  Photo courtesy of the U.S. Navy and Photographer's Mate 2nd Class Brett A. Dawson.

A:  Mass is a fundamental measure of inertia; it measures the resistance of the body to changes in its motion.  Thus, inertia is resistance to motion changes.  Whereas, momentum is mass in motion, and, is defined as the mass times the velocity.

Examples.  A girl (or a baseball) has a certain mass and, therefore, inertia.  She can directly feel her body's inertia as the resistance she encounters when she changes her body's momentum, such as when she:

• comes to a skater's stop, digging her blades into the ice, and feeling the ice pushing against her feet and legs, as she slows.
• stopped at the bottom, laboriously starts her bicycle up a steep hill.
• catches a fast baseball, stinging her hands, as the ball's momentum decreases abruptly to zero.

Momentum is an interesting quantity.  Within a given system, we can't change it.  Suppose a girl is poised at the bow of a canoe.  The girl-canoe system has a certain momentum.  She dives off the bow.  Does the canoe continue to sit in the water placidly?  No.  It shoots backward and, thereby, conserves momentum.  If the canoe has one-half the mass of the girl, then it shoots backward with twice the speed of the girl diving forward, and the system's momentum does not change.  

To change the system's momentum, we must exert a force on it that originates outside the system, and we have to exert the force for enough time.  Take the baseball, for example.  It just sits there in the pitcher's mitt, a 145-g mass with zero velocity.  It will continue that way forever unless something acts on it. 

To increase the ball's velocity, and, therefore, change its momentum, the pitcher must wind up, and, with considerable force, hurl the ball 50 mph (20 m/s) toward the catcher.  When the catcher stops the fastball, he exerts even a greater force than the pitcher did, because the stopping time is shorter than the hurling time.  That's why stopping the ball stings.  The ball's inertia, however, never changed; the ball remained a 145-g mass throughout the pitch and catch.  Only its momentum changed.

"Momentum is crucially important," says physicist Rod Nave, professor at George State University.  "It is a conserved quantity, and, as such, an indicator of one of the fundamental symmetries of the universe."

Further Reading:

Motion by Rod Nave, HyperPhysics

Conceptual Physics by Paul G. Hewitt

Inertia, Wikipedia

(Answered Sep. 19, 2006)