AP Physics 1 · Unit 4 · Momentum

Center of Mass Practice Problems

Find a system’s mass-weighted position and follow how that point moves. Practice loaded bars, masses on a coordinate plane, colliding carts, a recoiling guide, a separating projectile, and a person crossing a floating platform.

12 questions6 conceptual · 6 calculation

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Simulation scene from the Center of Mass lesson. — A scene from the related lesson. Open the practice to work through the questions.

What you’ll practice

Locate the center and predict its motion

Weight each position by mass

Include a uniform bar’s own mass, keep negative coordinates in a two-dimensional average, and distinguish a coordinate from a distance to another endpoint.

Connect system motion with external force

Use total momentum to find center-of-mass velocity. Compare rebound and sticking trials, internal force pairs, and a net external push.

Follow moving systems in a common frame

Include both objects’ kinetic energies for a recoiling guide. Separate shore-frame motion from walking speed relative to a floating platform, and conserve fragment momentum component by component.

A question from this set

Shape alone does not locate the center

Two straight rods have the same length. One has uniform density and cross section; the other contains more mass near its right end. Which statement about their centers of mass is correct?

Both centers of mass must be at the geometric midpoint because the lengths match.
The uniform rod’s center is at its midpoint; the other rod’s center shifts toward the greater mass concentration.
The nonuniform rod’s center must lie at its left end.

Try it in the practice set

Equal rod lengths do not guarantee equal mass distributions. Compare the uniform rod with a rod carrying more mass near its right end.

Key ideas

A mass-weighted point with a system-wide motion law

Symmetry works when the mass distribution is symmetric

A uniform rod has its center of mass at its midpoint. Extra mass near one end shifts that point. Multiplying all masses by the same factor leaves the center unchanged when positions stay fixed.

External force controls center-of-mass acceleration

For a fixed-mass system, total momentum is MvCM and the net external force is M aCM. Internal collisions and releases can change the parts’ motion while preserving the same center-of-mass motion.

See the physics

Watch the marker through an interaction

After checking an answer or calculation parts, run the prepared scene. Compare measured object and center-of-mass traces, watch a moving guide recoil, and follow the person to the platform’s moving far end. The marker and calculated values appear after an attempted run.

Use a hint for a starting point or open a worked solution to follow the reasoning. Your progress saves in this browser, so you can return to unfinished questions.

Ready for center of mass?

Begin with a conceptual question, then work through the calculations.

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