1. Angular Momentum and Torque

2. Goal of the class To understand angular momentum and torque
Question of the day: What direction is the torque when a seesaw is in motion?

3. Angular Momentum of a Particle
We define the angular momentum from the equation
L is along the axis of rotation
Ask about screw driver
Show arrowhead notation

4. Example Cylinder, M=2kg, R=10cm, ω=10rad/sec L=?
L=Iw =1/2MR2ω = 0.1kgm2/s

5. Practice Problem
A particle of mass 0.5 kg moves in the x-y plane. The position vector is given by:
What is the angular momentum of the particle about the origin?
L=mrxv
V=dr/dt =-6j
L=-9k kgm2/s
It’s -6t j not -6j
Show determinates and direct methods

6. Torque
I =MR2

7. Torque Torque is the rotational equivalent of force.
An unbalanced torque causes an angular acceleration
Find the torque
Not to be confused with work. You technically could use Joules, but we don’t we use Nm.
Torque = force x lever arm

8. The Sign of Torque
You will not learn how to do vector (cross) products yet:
The direction uses the ‘arrow’ notation
Into the board is shown as
Out of the board is shown as
You don’t need to learn that formula
Know which way a screw driver will screw and it tells you the direction.

9. Block and Pulley Mass of m Pulley has radius R and mass M NO SLIPPING
Mg-T = ma
τ=TR = Iα = Ia/R
T=Ia/R2

10. Block and Pulley
A uniform rod of mass M and length L is pivoted at one end, and is free to rotate in the vertical plane. If it is released from rest in a horizontal position.
What is the initial linear acceleration of the free end of the rod?
If a small object is placed on the free end of the rod before it’s released will the object stay in contact with the rod?
τ = Iα = MgL/2
T=Ia/R2
α = MgL2/2I a=Rα
I = ML2/3
a= 3g/2