4.2.2Linear Momentum
Momentum of a System — AP PHYSICS 1 Revision Notes & Topical Questions
5 min read 8 parts Lesson 9 of 13 1 quiz
Lesson summary
4.2.2 Momentum of a System — AP PHYSICS 1 notes: Calculate the total momentum of a system of objects and relate it to the motion of its centre of mass.System — any collection of objects treated together (two carts, a cannon and shell, a planet–moon pair).Total momentum — psys = Σ…
- One dimension
- Two dimensions
- Momentum link
- No external force
- Separation example
- Fnet,ext = Δpsys/Δt = Macm
Section 1 of 8Total momentum of a system
Total momentum of a system
System
- System any collection of objects treated together.
- (two carts, a cannon and shell, a planet–moon pair)
Total momentum
- Total momentum psys = Σmivi = m1v1 + m2v2 + …, a vector sum.
One dimension
- One dimension opposite directions have opposite signs.
Two dimensions
- Two dimensions add x and y components separately.
Section 2 of 8Centre of mass
Centre of mass
Centre of mass the point that moves as if all the mass were there and all external forces acted on it.
Position
- Position xcm = Σmixi / Σmi.
Velocity
- Velocity vcm = Σmivi / Σmi.
Momentum link
- Momentum link psys = Mvcm, with M the total mass.
No external force
- No external force the centre of mass moves at constant velocity whatever the internal interactions.
Separation example
- Separation example a shuttle and rocket separating in free space keep the same vcm.
Section 3 of 8Net external force
Net external force
Fnet,ext
Δpsys/Δt = Macm
- the net external force sets the rate of change of total momentum.
Skaters pushing apart on ice
- Skaters pushing apart on ice zero external force,
- so total momentum stays zero, the skaters gain equal and opposite momenta and the centre of mass stays still.
System including Earth
- System including Earth gravity is internal; a falling ball and Earth gain equal and opposite momentum.
Section 4 of 8Momentum and energy in systems
Momentum and energy in systems
Energy can change at constant momentum
- Energy can change at constant momentum internal forces do work, so skaters' kinetic energy rises from zero as chemical energy is converted.
Momentum can change at constant energy
- Momentum can change at constant energy a ball in uniform circular motion has constant kinetic energy but changing momentum.
- (external impulse)
Section 5 of 8Bookkeeping
Bookkeeping
Table
- Table columns for mass, initial velocity and final velocity of each object, then compute each momentum and sum.
Bar chart
- Bar chart total bar before equals total after for an isolated system;
- otherwise an external impulse or an error is present.
Object at rest
- Object at rest the total momentum is that of the moving object, and vcm = m1v1/(m1 + m2).
Perfectly inelastic collision
- Perfectly inelastic collision both objects move at vcm, since a collision cannot change vcm.
More objects
- More objects keep adding terms; track which mass is in the system at each instant.
Section 6 of 8More from the specification
More from the specification
Centre of mass velocity speed
- Centre of mass velocity speed isolating colliding bodies preserves total momentum, ensuring the system centre of mass maintains constant speed.
Vertical component
- F sin θ for an angle θ to the horizontal.
Explosion
- Interaction pushing parts of a system apart.
Section 7 of 8Key terms
| Term | Meaning |
|---|---|
| System | Chosen group of objects analysed together. |
| Total momentum | Vector sum of all momenta in the system. |
| Centre of mass | Point that moves as if all mass and external forces were there. |
| Net external force | Vector sum of forces from outside the system. |
Section 8 of 8Exam technique
1
Adding speeds instead of signed velocities.
2
Assuming total momentum is zero whenever the centre of mass is at rest without checking external force.
3
Using the mass of only one object in Mvcm.
4
Including internal forces when finding the net external force.
5
Leaving out an object that moves in the system.
Marked practiceQuizzes for this lesson
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