NM Unit 8Topic(s): Angular

MomentumLearning Goals:Adapt linear collision analysis for rotational collision analysisDevelop a solution strategy to solve problems involving torques and change in angular momentumDescribe how angular momentum of a system changes as a result of interactions with other objects or systemsSolve problems involving angular momentum

Connections Back to Unit 7

Momentum will be conservedThere is a connection between mass and velocityWe will have an impulse-momentum theoremCollisions will only be inelastic for rotational motion (collision between two rotating bodies)

Product of angular velocity and moment of inertia.

can you see the connection back to unit 7?

Conservation of Angular Momentum

Once an object is set spinning it can change its angular velocity by having another force applied to it OR by changing its moment of inertia.This change in I results in a change in omega.

Analysis of previous clip

once Sam brings his legs in his mass is located by his axis of rotation, so his moment of inertia drops.Since angular momentum is conserved, his rotational velocity must increase (and it does!)This is why divers/gymnasts/ice skaters spin faster when in a more compact configuration.

New Look Impulse-Momentum

If I want to increase or decrease the angular momentum of an object it must have an angular acceleration.A torque can cause this

A 1kg hollow sphere with a radius of 0.08m (I=2/3MR^2) is rotating at 45 rad/s. A force of 6N is tangentially applied to the sphere for 0.04s. What is the new angular velocity of the sphere?