Angular Momentum and Torque

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Presentation transcript:

Angular Momentum and Torque

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?

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

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

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

Torque I =MR2

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

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.

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

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