# Impulse and Momentum

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## Video Clips

#### Conservation of Momentum

RealVideo®
6:29 minutes (0:00 - 6:29)

Definitions, including p = mv and F = dp/dt.

Instructor: Prof. Walter Lewin
Prior Knowledge: Force

#### Impulse

RealVideo®
9:38 minutes (11:52 - 21:30)

Definition, including impulse as δp and F/δt; impact times and forces.

Instructor: Prof. Walter Lewin
Prior Knowledge: Momentum (Beginning of V15)

RealVideo®
2:38 minutes (21:30 - 24:08)

Dropping a tennis ball on top of a basketball causes the tennis ball to bounce very high.

Instructor: Prof. Walter Lewin
Prior Knowledge: Impulse (11:52 of V17)

#### Impulse and Thrust

RealVideo®
7:31 minutes (24:08 - 31:39)

Throwing objects produces recoil; comparison of recoil to thrust; calculation of rocket thrust for Saturn rocket.

Instructor: Prof. Walter Lewin
Prior Knowledge: Impulse (11:52 of V17)

## Lecture Notes

#### Momentum

PDF - 1.6 MB#
Page 1 to page 4

Definition of momentum (p = m*v); Newton's laws and momentum; law of conservation of momentum of a particle and of a system of particles, with examples; relationship between forces and momentum; elastic and inelastic collision, with examples.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Newton's Laws

#### Impulse and Collisions

PDF#
Page 1 to page 6

Definition of impulsive force, with example; elastic and inelastic collisions, with examples in one-dimension and two-dimensions.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Momentum, Conservation of Energy

#### Momentum

PDF - 1.5 MB#
Page 1 to page 9

Definition of momentum (p = m*v); Newton's laws and momentum; Law of conservation of momentum of a particle and of a system of particles, with examples; relationship between forces and momentum; elastic and inelastic collision, with examples.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Newton's Laws

#### Impulse and Collisions

PDF - 1.2 MB#
Page 2 to page 16

Definition of impulsive force, with example; elastic and inelastic collisions, with examples in one-dimension and two-dimensions.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Momentum, Conservation of Energy

#### Power and Momentum

PDF
Page 1

Power defined, with equation (P = F*v); impulse defined; center of mass defined; velocity and momentum of center of mass.

Instructor: Dr. George Stephans
Prior Knowledge: Momentum

#### Newton's First Law

PDF#
Page 5 to page 7

Definition of inertial mass; standard kilogram; definition of momentum (p = m*v).

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: One Dimensional Motion

#### Newton's Second Law

PDF#
Page 8 to page 12

Definition of force (F=ma); superposition principle; definition of impulse and average impulse; Newton's second law equations for force, acceleration, momentum.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Newton's First Law, derivatives, integrals

#### Conservation of Momentum

PDF
Page 1 to page 27

Definition of momentum (p = m*v) and impulse; non-constant force and impulse; conservation of momentum; translational motion of the center of mass; modeling external forces and conservation of momentum; modeling of instantaneous collisions; momentum diagrams and equations.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Newton's Laws

#### Collision Theory

PDF#
Page 1 to page 20

Momentum and impulse equations; definition of conservation of momentum for an isolated system; momentum problem solving strategies; momentum diagram and equations; planar collision theory; elastic collisions; 2D elastic collision example problem.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Lecture 19

#### Linear Momentum Review

PDF
Page 1 to page 8

Momentum and change of momentum defined, with equations; strategies for solving momentum and impulse problems; collisions and conservation of momentum; center of mass.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: Lectures 19, 21

## Practice Problems

#### Energy and Momentum

PDF
Problem 1 to problem 1

Friction and acceleration; which forces must be known to solve for energy and momentum; kinetic energy and momentum in a collision. Solution not included.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Kinetic Energy and Impulse

PDF
Problem 3

Kinetic energy of two blocks of unequal mass that experience the same impulse. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Momentum and Stopping Force

PDF
Problem 4

Distance needed to stop a ping-pong ball and a bowling ball, which have the same initial momentum. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Momentum of Isolated Systems

PDF
Problem 4 to problem 8

Concept questions about conservation of momentum in isolated systems of one or more bodies. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Impulse and Momentum

PDF
Problem 3

Motion of a ball falling and bouncing off of the ground.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Impulse and Momentum

PDF
Problem 1

Force acting on the ankle of a person jumping to the ground from a height.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Space Shuttle Acceleration

PDF#
Problem 9

Finding fuel mass used for shuttle acceleration.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Saturn V Rocket

PDF#
Problem 10

5-part impulse problem; calculating velocity, acceleration, burn time for rocket.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Delivering Impulse to a Rod

PDF#
Problem 9

A rod is hit off-center; finding velocity, ω, position, and kinetic energy.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Going to the Sun

PDF#
Problem 3

7-part orbit problem; finding impulses to allow spacecraft to reach sun.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

## Exam Questions

#### Impulse for a Bouncing Ball

PDF#
Problem 12

6-part problem; p of ball before and after hitting floor; average force and impulse; change in kinetic energy.

Instructors: Dr. Peter Dourmashkin, Prof. Kate Scholberg
Prior Knowledge: None