1. Collisions Momentum: a measure of motion
Force: a cause of change in motion
What changes when a force is applied?
Linear Momentum: p ≡ mv (vector!!!!!)
the tendency of an object to pursue straight line motion
Impulse: the change in motion
“Impulse Power” ?

2. Conservation of momentum
two (or more) bodies + action/reaction + no external forces
FAB = - FBA
→ equal but opposite impulses!
→ pA + pB = 0
When the net external force on a system is zero, the total momentum of that system is constant.
p1 + p2 + p is constant
Collisions, explosions etc: m1v1 + m2v2 =m1v’1 + m1v’2
Cart Demo's
Elastic = kinetic energy is also conserved
Inelastic = kinetic energy is lost (some “stickiness”)
Completely Inelastic =maximal Kinetic Energy Loss (masses stick together)
Superball Demo
Application to Bumper Cars

3. What plays the role of mass, force, momentum, etc?
Rotations
Rotational Kinematics
In close analogy with linear motion with constant acceleration
𝐿𝑖𝑛𝑒𝑎𝑟𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐴𝑛𝑔𝑢𝑙𝑎𝑟𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑥 θ 𝑣 ω 𝑎 α
What plays the role of mass, force, momentum, etc?

4. Rotational Inertia: like mass from linear motion
Rotational Kinetic Energy
for a single point particle
for a solid rotating object
Moment of Inertia
I = moment of Inertia = rotational inertia
I =  mr2 = m1r12 + m2r22 + m3r
Rotational Inertia depends upon how the mass is distributed
Rotational Inertia: like mass from linear motion
F = ma becomes t = Ia where t is the torque (twisting version of force)

5. L L R2 R a b a b R R

6. angular momentum (chair) angular momentum (precession)
Torque: the rotational analogue of force
Torque = force x moment arm
 = Fr┴=F r sin 
moment arm = perpendicular distance through which the force acts
r ┴
r ┴
q=90° q F F
r ┴ q F
𝐿𝑖𝑛𝑒𝑎𝑟𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐴𝑛𝑔𝑢𝑙𝑎𝑟𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑚 𝐼 𝑎 α 𝐹 τ 𝑝 𝐿
τ=𝐼α 𝐾𝐸 𝑟𝑜𝑡 = 1 2 𝐼 ω 2 𝐿=𝐼ω
Demo:
torque (gyro)
angular momentum (chair)
angular momentum (precession)
Assignment: Tilt-A-Whirl!

7. Oscillations Equilibrium “restoring force”
example: spring, where F = -kx
plus Inertia
mass
→ Oscillations
Periodic Motion
motion that repeats
T = period for one full cycle of motion
frequency
number of cycles per unit time
angular frequency w
radians per unit time
𝑓= 1 𝑇
ω=2π𝑓= 2π 𝑇

8. Simple Harmonic Motion of a mass on a spring
A is the amplitude of the motion (maximum displacement from equilibrium)
motion can be thought of as projection of uniform circular motion
SIMULATION!
𝑥=𝐴cos 2π 𝑇 𝑡 =𝐴cos ω𝑡
𝑥=𝑟cos θ 𝑤𝑖𝑡ℎθ=ω𝑡,𝑟=𝐴 𝑣 𝑇 =ω𝑟, 𝑣 𝑥 =− 𝑣 𝑇 sin θ =− 𝑣 𝑇 sin ω𝑡 𝑎 𝑐𝑝 =𝑟 ω 2 , 𝑎 𝑥 =− 𝑎 𝑐𝑝 cos θ =− ω 2 𝑟cos θ 𝑠𝑜 𝑎 𝑥 =− ω 2 𝑥 𝑚𝑎𝑠𝑠−𝑠𝑝𝑟𝑖𝑛𝑔𝑠𝑦𝑠𝑡𝑒𝑚 𝐹=−𝑘𝑥=𝑚𝑎 𝑠𝑜 ω= 𝑘 𝑚 so 𝑓= 1 2π 𝑘 𝑚
Amplitude does not affect frequency!

9. mass m on a string of length Lx s mg T
Fnet L
The Simple Pendulum
mass m on a string of length L
This is a small angle approximation
Example: How long should a pendulum be in order to have a period of 1.0 s?

10. Physical Pendulum, center of gravity mg d sin I sin 
More SHO variations
Physical Pendulum, center of gravity
mg d sin I
sin 
-mg d Ia
→ 
Torsion Pendulum-demo
= -  = I 
w = ?
Pirate Ship Swing Ride Worksheet