University Physics Volume 1

# Summary

### 9.1Linear Momentum

• The motion of an object depends on its mass as well as its velocity. Momentum is a concept that describes this. It is a useful and powerful concept, both computationally and theoretically. The SI unit for momentum is kg$··$ m/s.

### 9.2Impulse and Collisions

• When a force is applied on an object for some amount of time, the object experiences an impulse.
• This impulse is equal to the object’s change of momentum.
• Newton’s second law in terms of momentum states that the net force applied to a system equals the rate of change of the momentum that the force causes.

### 9.3Conservation of Linear Momentum

• The law of conservation of momentum says that the momentum of a closed system is constant in time (conserved).
• A closed (or isolated) system is defined to be one for which the mass remains constant, and the net external force is zero.
• The total momentum of a system is conserved only when the system is closed.

### 9.4Types of Collisions

• An elastic collision is one that conserves kinetic energy.
• An inelastic collision does not conserve kinetic energy.
• Momentum is conserved regardless of whether or not kinetic energy is conserved.
• Analysis of kinetic energy changes and conservation of momentum together allow the final velocities to be calculated in terms of initial velocities and masses in one-dimensional, two-body collisions.

### 9.5Collisions in Multiple Dimensions

• The approach to two-dimensional collisions is to choose a convenient coordinate system and break the motion into components along perpendicular axes.
• Momentum is conserved in both directions simultaneously and independently.
• The Pythagorean theorem gives the magnitude of the momentum vector using the x- and y-components, calculated using conservation of momentum in each direction.

### 9.6Center of Mass

• An extended object (made up of many objects) has a defined position vector called the center of mass.
• The center of mass can be thought of, loosely, as the average location of the total mass of the object.
• The center of mass of an object traces out the trajectory dictated by Newton’s second law, due to the net external force.
• The internal forces within an extended object cannot alter the momentum of the extended object as a whole.

### 9.7Rocket Propulsion

• A rocket is an example of conservation of momentum where the mass of the system is not constant, since the rocket ejects fuel to provide thrust.
• The rocket equation gives us the change of velocity that the rocket obtains from burning a mass of fuel that decreases the total rocket mass.