Chapter 8

Rotational Motion

Why rotational?

• We’ve focused on translational motion up to this point

• Rotational motion has things in common with translational motion

• Examples: spinning wheels,

washing machine drum,

merry-go-round, etc.

Angular Quantities

Quantities in linear motion have a corresponding quantity in rotational motion

Angular Position

Angular displacement is the angle (in rads) through which a point or line has been rotated about an axis

Angular Velocity

The rate of change of angular displacement ΔӨ

with time Δt

Instantaneous Angular Velocity

Angular Acceleration

Instantaneous Acceleration

The rate of change of angular velocity

Period

• The time it takes to complete one cycle or revolution. Also the reciprocal of the frequency.

T=1 f

The equations of motion for constant angular acceleration are the same as those for linear motion, with the substitution of the angular quantities for the

linear ones.

Look familiar?!

TorqueFrom experience, we know that the same force will be much more effective at rotating an object such as a nut or a door if our hand is not too close to the axis.

This is why we have long-handled wrenches, and why doorknobs are not next to hinges.

To make an object start rotating, a force is needed

A longer lever arm is very helpful in rotating objects.

Torque

Torque is calculated

• Torque depends on

–The length of the lever arm r┴

–The force applied F

Only the tangential component of force causes a torque

Moment of Inertia

• The rotational equivalent of mass

• Symbolized with letter I

Angular Momentum

Angular momentum-the product of the angular velocity of a body and its moment of inertia about the axis of

rotation. Depends on the mass of the object and how it is distributed

Rotational Kinetic Energy

We have learned that the kinetic energy of an object is

By substituting the rotational quantities, we find that the rotational kinetic energy is:

An object that has both translational and rotational motion must take both into account to find the total KE

Rotational Kinetic Energy

Torque does work as it moves the wheel through an angle θ:

A torque acting through an angular displacement does work, just as a force acting through a

distance does.

The work-energy theorem still applies!

Vector Nature of Angular Quantities

We have considered the magnitude of the angular quantities but must also define the direction!

The angular velocity vector points along the axis of rotation; its direction is found using a right hand rule:

1. Curl fingers around the axis in the direction of rotation

2. Thumb is pointing in direction of ω

Vector Nature of Angular Quantities

Angular acceleration and angular momentum vectors also point along the axis of rotation.

• Giancoli, Douglas. Physics: Principles with Applications 6th Edition. 2009.

• Walker, James. AP Physics: 4th Edition. 2010

• Zitewitz. Physics: Principles and Problems. 2004

• www.hyperphysics.com• http://whs.wsd.wednet.edu/Faculty/Bus

se/MathHomePage/busseclasses/apphysics/studyguides/chapter7_2008/Chapter7StudyGuide2008.html

References

22