Vector Cross Product Torque Rotational Dynamics PHYS116 A02

Vector (Cross) Product, Torque, Rotational Dynamics PHYS-116 A-02, 10/14/10, Lecture 14 Momchil Velkovsky

The vector product

Torque ¡ ¡ A force applied at a right angle to a lever will generate a torque. The distance from the pivot to the point of force application will be linearly proportional to the torque produced.

The four forces shown all have the same magnitude: F 1 = F 2 = F 3 = F 4. Which force produces the greatest torque about the point O (marked by the blue dot)? F 1 1. 2. 3. 4. 5. F 1 F 2 F 3 F 4 not enough information given to decide F 3 O F 2 F 4

Lines of force and calculations of torques ¡ The directions of torques produced will give us another opportunity to apply the right-hand rule (RHR).

A force acts an object at a point located at the position What is the torque that this force applies about the origin? 1. 2. 3. 4. 5. zero

Calculate an applied torque

Τ = Iα is just like F = ma—calculate alpha

Torque and a cable about a pulley

Another look at the unwinding cable

A rigid body in motion about a moving axis

Rolling with and without slipping • Rolling with slipping may be calculated. Slipping makes things worse (for driving and calculations).

Consider the speed of a yo-yo toy

The race of objects with different moments

Rolling ball down a ramp v. CM CM r P l q Free body diagram y CM a. CM Fg N P fs x z h

Three ways to solve the rolling ball motion

Three ways to solve the rolling ball motion

Three ways to solve the rolling ball motion

Reading for next time Chapter 11. 7 – 11. 12