Chapter 9

Question 1

Linear Momentum formula

Answer 1

p= mv (mass times velocity)
Momentum is a vector
units: kg m/s

Question 2

Total Linear Momentum

Answer 2

P total = P1 + P2 = m1v1 + m2v2
can also break into vector components
* total momentum of any collection of particles is equal to the total mass times the velocity of the COM point

Question 3

Relation between kinetic energy and momentum

Answer 3

K = P^2 / 2m

Question 4

Newtons Second Law

Answer 4

not external force = rate of change of momentum
F = dP / dt Or F = change in P / t
* when mass is constant

Question 5

what is Impulse and formula

Answer 5

Change in momentum: (triangle) p= Ft = I
Change in momentum = total impulse from external forces
It is area under Ft graph
average force is th econstant force that would produce the same impulse: I = Ft

Question 6

Impulse and Momentum Theorem

Answer 6

Impulse of the force acting on a particle equals the change in the momentum of the particle

Question 7

Impulse Approximation

Answer 7

During short intense interactions the contact (interaction) force (normal force) larger than others
Then impulse equals the integrate over the contact time only

Question 8

Newtons 3rd Law - Conservation of Momentum

Answer 8

New toms 3rd Law - F21=F12
Momentum changes are equal and opposite
Total momentum p is constant: P= P1+ P2
Momentum doesn’t change: CP = CP1 + CP2 = 0
Note: only internal forces act, external forces would transfer momentum into or out of system

Question 9

Conservation of Momentum

Answer 9

for an isolated system: Pf = Pi
total moment after an interaction is equal to the total momentum before the interaction

Question 10

Work and Impulse - graphs

Answer 10

Work is area under F vs x graph: W= (triangle) K
Impulse is area under F vs t graph: I= (triangle) p

Question 11

Collisions - What is it

Answer 11

brief interaction between two+ objects (interaction time is short relative to rest of motion)
During collision - objects exert equal and opposite forces on each other
Assume internal forces are much langer then any external forces on the system
Ignore external forces if we compare velocities just before and just after the collision
Total momentum is conserved

Question 12

Elastic Collision

Answer 12

Total kinetic energy is the same before and after

Question 13

Inelastic Collision

Answer 13

Kinetic Energy is lost - converted into other forms of energy

Question 14

Completely Inelastic Collision

Answer 14

When two colliding objects stick together and more together after collision
Kinetic energy is lost in this collision converts to other forms

Question 15

Apply Newtons laws to extended objects
Translational vs Rotational

Answer 15

Translational motion: force from anywhere
Rotational motion: force furthest from center of mass (COM is pivot point)

Question 16

Motion of the center of mass

Answer 16

It is the same as if the object were a single particle at the COM with all external forces applied directly to it

Question 17

General motion of a rigid body

Answer 17

Translation of the center of mass plus rotation about center of mass
When axis of rotation is not fixed (ie not pure rotation about a fixed axis)

Question 18

Pure Rolling Motion

Answer 18

An object rolls without slipping

Question 19

Combination motion

Answer 19

An object rotates about an axis that is moving along a straight line

Question 20

Rolling Motion

Answer 20

Different points on a rolling object have different velocities
Velocity of each particle is the velocity of the center plus the tangential velocity of that point relative to the center
V = VCM + Vt
Note: Point in contact with the ground is momentarily stationary
- Point on top of wheel moves forward at twice the speed of center
- If body rolls without slipping then angular velocity and angular acceleration are related to linear velocity and tangential acceleration of the center
– V= Rw and accelera = R angular accelera

Question 21

Friction and Rolling Resistance

Answer 21

• Friction necessary to create a torque which can cause rotation and rolling
• static friction if wheel rolls without slipping
• at point of contact between road and wheel theres no relative motion and friction does no work
• Rolling resistance - slows the wheel results from the tire flexing inelastically at the contact point

Question 22

Angular Momentum definition

Answer 22

• the rotational analogue of linear momentum
• measures the quantity of rotation
• symbol: L
• units! Kg m^2/s
• product of moment of inertia and angular velocity: L= I*w
  ^ formula for angular momentum for rigid body

Question 23

Newtons and law for rotation

Answer 23

_ torque due to external forces is equal to rate of change of L
- T = dL/dt

Question 24

Conservation of Angular momentum

Answer 24

In an isolated system (no external torque) the total angular momentum is constant
- Lf = Li

Question 25

Angular Momentum Vector

Answer 25

- For symmetrical rotating rigid body vector L will be along the axis of rotation parallel to vector w - L= I*w (generally L is not parallel to w but I*w is equal to component of L along the rotation axis)

Question 26

Angular Momentum of a particle

Answer 26

- L is a vector - like torque - depends on the choice of origin (or pivot) - If particles motion is all in xy plane then L is parallel to the z axis - L= r x p = r x (mv)

Question 27

Angular Momentum in vector notation

Answer 27

- mass m moving with linear momentum p in a circle the angular momentum L is given by L = r x p |L|=|r||p| sin 0