physics 218: lecture 14

Physics 218 Fall 2010 Slide 1

Physics 218: Lecture 14

Chapter 8: Rotational Motion

Torque and Newton’s Law Moment of inertia

Physics 218 Fall 2010

Physics 218 Fall 2010

Supposing two people of equal strength grab onto either side of this tire and pull. What would the free body diagram look like? What could you say about the motion of the object?

Physics 218 Fall 2010

mF

a

Supposing two people of equal strength grab onto either side of this tire and pull. What would the free body diagram look like? What could you say about the motion of the object?

0

0No acceleration => constant velocity

Physics 218 Fall 2010

Supposing two people of equal strength grab onto either side of this tire and pull this way. What would the free body diagram look like? What could you say about the motion of the object?

Physics 218 Fall 2010

mF

a

Actually the same free body diagram applies …

0

0 No acceleration => constant velocity

… for the center of mass

Physics 218 Fall 2010

The thing that is different is that there is now a torque that produces rotation about a pivot point. Torque and rotational motion are the topics this week.

Physics 218 Fall 2010

Physics 218 Fall 2010

We’ll need to describe the rotation of objects

The whole object rotates as one, so it is sufficient to know the axis of rotation and the angle,

Physics 218 Fall 2010

This is equivalent to the way we have described linear motion up to now

x

x

And, if you understand linear motion, there is a rich set of analogies to exploit

Physics 218 Fall 2010

x

Linear motion Rotational motion

position x

tva

acceleration

velocity txv

amF

angle

t

angular

acceleration

angularvelocity t

I

Physics 218 Fall 2010

Quiz

An object experiences zero net torque. Which of the following statements is true?

Hint: zero net torque is analogous to zero net force.

A.The object is not rotating.B.The object is rotating.C.The object has zero angular velocity. D.The object has constant angular velocity.E. All statements are false, including this one.

Physics 218 Fall 2010

Relationship between rotation and linear motion

In rotational motion, all points travel on a circle around the axis of rotation.

Physics 218 Fall 2010

Relationship between rotation and linear motion

rs s distance traveled

around arc

r radial distance to center of rotation

angle in radians

s

Physics 218 Fall 2010 15

Demo 1Q-1: Rotational Motion

Same angular distance.

rs

Physics 218 Fall 2010

(rad)

180

(degrees)

Convert 60 degrees from degrees to radians :

0472.13

60180

radian

Physics 218 Fall 2010

distance along arc

rs

raacceleration

velocity rv

Rotational motion

tv

angle

angularvelocity

angularacceleration

t

Basically, to get the linear quantity, take the angular quantity (in radians) and multiply by r.

Linear motion

s

Physics 218 Fall 2010

Quiz

A wind turbine spins at 22 rpm (rotations per minute). The blades are 20 m long. What is the linear speed at

the tip of the blade?

A. 1.1 m/sB. 7.3 m/sC. 77 m/sD. 46.1 m/s

Physics 218 Fall 2010 19

Quiz - CD PlayersLinear speed of the disk where the laser shines must be

maintained at a constant value of 1.25 m/s.

Does the disc spin faster when it is reading the inner or outer tracks on the disc?

A. Inner

B. Outer

Physics 218 Fall 2010 20

Quiz

Image from www.jackiechankids.com/ files/ATW.htm

R4R

Is the linear velocity at the very top of the rear wheel:

A. greater thanB. equalC. less than

the linear velocity at the top of the front wheel?

FrontWheel

RearWheel

Physics 218 Fall 2010 21

TorqueTorque, , is the rotational analog to Force.

F ma ITorque, , involves a force, F

The ability of a force to rotate an object depends on not only the magnitude of the force, but also depends on

-where the force is applied

-the direction in which the force is applied.

rF

Physics 218 Fall 2010 22

Torque

The ability of a force to rotate an object depends on not only the magnitude of the force, but also depends on

-where the force is applied

-the direction in which the force is applied.

Physics 218 Fall 2010 23

Torque

Forces along the radial direction produce no torque..

The component prependicular to r produces torque.

rF

sinFF

Physics 218 Fall 2010 24

Newton’s Second Law

F ma I

The moment of inertia, I, appears as a rotational mass.