Ro

tati

on

al M

oti

on

Deg, Rad, GradThere are 360 degrees in one rotation of a circe.

There are 2π radians in one rotation of a circle.

There are 400 gradians in one rotation of a circle.

Convert between radians and degrees to fill in the missing measurements below.

Angular Displacement, Velocity, and Acceleration.

Angular Displacement (θ): The change in angle (in radians) of a rotating object.

Angular Velocity (ω): The rate at which an object is spinning. Rad/s

Angular Acceleration (α): The rate at which a spinning object is changing speed. Rad/s2

A Couple other useful formulas.

ra rArcLength

Lever Arm: The perpendicular distance from the axis of rotation to the point where the force is exerted.

Torque: A measure of how effective a force causes rotation.

Torque = Force perpendicular to rotation times distance away from the center of rotation.

Measured in N·m

Also seen as

when the force is not applied at a right angle to the lever arm.

Rotational Dynamics & Torque

rF

Label each of the situations in rows a and b as having ‘No’, ‘Little’, or ‘Maximum’ effect.

sinrF

The lug nut on your car needs to be torqued to 81.0 N·m. You have a wrench that is 25.0 cm long and you push at the angle indicated in the picture. With what force do you need to push to correctly torque the nut?

Moment of InertiaMoment of Inertia: Resistance to rotation

Mo

men

ts o

f In

erti

a fo

r V

ario

us

Ob

ject

s

Center of Mass – the point at which the entire mass of a body may be considered concentrated.

Equilibrium: 1) Sum of all forces equals zero. 2) Sum of all torques equals zero.