MA High School Introductory Physics MCAS Module 3 momentum and collisions: a complete overview of momentum, impulse, conservation of momentum, elastic and inelastic collisions, crash safety, and circular motion

What Module 3 actually demands

Module 3 tracks momentum through interactions, the second big quantity (after position and velocity) the course builds on. Under the Massachusetts STE framework it sits in the Motion and Forces reporting category, and it carries two of the named standards: conservation of momentum (HS-PS2-2) and the crash-safety engineering design (HS-PS2-3). The standards lean on using mathematics (the before-equals-after equation) and designing solutions (safety devices), with the crosscutting ideas of systems and cause and effect.

This guide ties together the matching dot-point pages, each with its own practice questions: momentum and impulse, conservation of momentum, collisions and explosions, crash safety and engineering design, and circular motion and centripetal force.

Momentum and impulse

Momentum is mass times velocity, $p = mv$, a vector in kg m/s. Impulse is a force over a time and equals the change in momentum. The practical message is that a fixed change in momentum can come from a big force briefly or a small force for longer, which is the seed of all the crash-safety reasoning. Watch direction: when an object bounces back, its velocity reverses sign, so the change in momentum is larger (about double) than for simply stopping it.

Conservation of momentum

Conservation of momentum (HS-PS2-2) says that with no external force, total momentum before an interaction equals total momentum after: $p_{before} = p_{after}$. It follows from Newton's third law (equal and opposite impulses). The method is always the same: choose a positive direction, sum $mv$ before and after with signs, set them equal, and solve. Objects that stick move off as one combined mass; recoils and explosions start at a fixed total (often zero) and produce equal and opposite momenta. This conservation law is not on the reference sheet, so you recall it.

Collisions and explosions

A collision is elastic if kinetic energy is conserved (the objects bounce) and inelastic if kinetic energy is transformed into heat, sound, and deformation, with perfectly inelastic meaning the objects stick. The key separation: momentum is conserved in all collisions (no external force), but kinetic energy only in elastic ones. Real crashes are inelastic, conserving momentum and total energy but losing kinetic energy. A recoil is a collision in reverse, with the lighter object flying off faster.

Crash safety and engineering design

The engineering-design standard HS-PS2-3 applies impulse to safety. A person in a crash must lose all their momentum, so the change in momentum is fixed; safety devices extend the stopping time, and a fixed momentum change over a longer time means a smaller force. Crumple zones, airbags, seatbelts, helmet padding, and foam mats all work this way. A good evaluation names the longer time and the smaller force explicitly, rather than just calling the device "soft."

Circular motion and centripetal force

An object moving in a circle constantly changes the direction of its velocity, so it is accelerating even at constant speed, and that acceleration points toward the center. The net inward force needed is the centripetal force, which is not a new force but the role played by a real force: tension, friction, gravity, or a normal force. Remove the inward force and the object moves off in a straight line tangent to the circle, by Newton's first law, not radially outward.

Check your knowledge

A mix of recall, calculation, and explanation questions covering Module 3. Attempt them under timed conditions, then check against the solutions.

1. A $2.0$ kg object moves at $6.0$ m/s. Calculate its momentum. (2 marks)
2. State what impulse is and what it changes. (2 marks)
3. State the law of conservation of momentum. (2 marks)
4. A $4.0$ kg cart at $3.0$ m/s sticks to a stationary $2.0$ kg cart. Calculate their common velocity. (2 marks)
5. State which quantity is conserved in all collisions and which only in elastic collisions. (2 marks)
6. A car crash is inelastic. State what happens to the kinetic energy. (1 mark)
7. Explain how a crumple zone reduces the force on passengers. (2 marks)
8. A passenger's change in momentum is the same with or without an airbag. What does the airbag change? (1 mark)
9. State the direction of the centripetal force on an object moving in a circle. (1 mark)
10. A ball on a string is whirled in a circle and the string breaks. Describe the ball's subsequent motion. (1 mark)