Chapter 8 Rotational Motion

Rotational Motion

- In physics we distinguish two types of motion for

objects - Translational Motion (change of location)
- Rotational Motion (change of orientation)
- Weve mostly discussed translational motion

today we consider rotation.

Circles

- Circumference is distance around the perimeter of

the circle. - Small circle is half the radius so half the

diameter and half the circumference.

Radius

Diameter

Axis

Radius

Diameter

Axis

Circular Motion

- Rotational Speed Revolutions per second
- Tangential Speed Total distance per second

Same Rotational Speed Different Tangential Speeds

Check Yourself

- A pair of wheels are connected by a chain.
- Which wheel has higher
- rotational speed?
- By how much?
- Faster tangential speed on rim?

Bicycles

Notice how gears work on a modern bicycle

Simple Complex Objects

- Motion of simple objects Position
- Motion of complex objects Position Rotation

Axis of Rotation

COMPLEX

SIMPLE

Inertia

- Mass is a measure of inertia for linear motion.
- Rotational inertia is similar concept for

rotation.

Gold brick

Normal brick

M

m

Easy to move

Difficult to move

Wood Bat

Plastic Pee-wee Bat

x

x

Difficult to Rotate

Easy to Rotate

Rotational Inertia

- Rotational inertia depends on
- Total mass of the object
- Distribution of the mass
- Farther the mass is from the axis of rotation,

the larger the rotational inertia. - Rotational inertia goes as (mass) x (distance)2

Demo Inertia Sticks

- Two metal pipes of the same mass

Rotate

Check Yourself

- Which dancer has greater rotational inertia?

Axis of Rotation

A

B

Demo Hammer Balance

- When is the hammer easier to balance on your

finger?

Demo Drop the Stick

- Two meter sticks stand upright against a wall

one has a hunk of clay on the end. - Which stick will swing down and hit the floor

first? - Why?

Demo Long Legs

- Long legs have greater rotational inertia than

short legs so long legged animals have a slow

walking stride.

Demo Ramp Racing

- The two disks and rods have the same mass but one

has connecting rods near the center while the

other has rods near the rim. - When rolled down a ramp, which wins the race?

Demo Hoop Disk Racing

- Roll a hoop and a disk down a ramp which wins

the race?

Torque

- When a force causes a rotation, we identify this

as a torque. - Torque depends on
- Magnitude of Force
- Direction of Force
- Lever Arm
- (Torque) (Force) x (Lever Arm)

Lever Arm

Lever arm is perpendicular distance from axis of

rotation to the direction of the force.

Check Yourself

- Identify the lever arm for each wrench.

Force

Force

Which wrench design gives the most torque?

Torque for a Pirouette

- The farther the distance between the feet, the

greater the lever arm so the greater the torque

for creating the rotation.

Push on Floor

Reaction Force

Lever Arm

Feet apart

Feet together

Check Yourself

- In which case are you exerting more torque?

A

B

Balance of Torques

- Torques clockwise and counter-clockwise balance

in both cases since - (250 N) x (3 m) (500 N) x (1.5 m)

Her lever arm is 3 meters

Center of Mass/Gravity

- Average position of all the mass in an object is

called the center of mass (CM). - Average position of the weight distribution is

called the center of gravity (CG). - When gravity is constant these two locations are

the same.

Locating Center of Gravity

- Balance an object to find center of gravity

Center of Gravity

Demo Balance the Can

- If a small amount of water is added to an empty

soda can then the can may be balanced on its

bottom edge.

PEPSI

CG

x

Stability

- Object is stable if CG is above the base.

STABLE

CG

CG

UNSTABLE

Weight

Weight

Axis

BASE

BASE

Axis

Check Yourself

- Three trucks
- are parked on
- a slope. Which
- truck(s) tip
- over?

CG

CG

CG

Balance Ballet

The force of gravity and the support force of the

floor can balance only when a dancers center of

gravity is located above the base of support.

Center of Gravity located above the dancers toe

Balance Beam

- You tend to hold your arms out when on a balance

beam for two reasons - Increase your rotational inertia so as to slow

your rate of tipping over. - Allow rapid changes of your center of gravity, to

regain balance

Demo Balanced Bird

- Where is the birds center of gravity?

Demo Mystery Wheel

- Wheel doesnt roll down hill. How is that

possible?

Centripetal Force

- Centripetal means towards the center.

Whenever an object moves along a circular path

there must be a force on that object in the

direction of the center of the circle.

In such a case, the force is said to be

centripetal.

Check Yourself

- Object rotates in a circle on the end of a

string. Is there a force on the object? - What causes the force?
- In what direction is the force?

Centripetal Force Examples

Demo Around the Ring

- The support force exerted by the wall of the ring

is centripetal. - Ball moves in a straight line once the force is

removed (ball leaves the ring).

Support Force

Magnitude of Centripetal Force

- Magnitude of centripetal force is large when
- Speed is large
- Radius is small
- Mass is large

Hurricanes

Hurricanes strength (wind speed) depends on how

low the pressure gets in the center.

F

H

L

H High Pressure L Low Pressure F

Centripetal Force due to pressure difference

Rita, 9/22/05

Demo Loop-the-Loop

If the speed of the ball is large then the

support force of the track is required to keep it

moving in a circle.

Release

Velocity

This is also a good demo for conservation of

kinetic potential energy.

Demo Loop-the-Loop

Ball could even circle a loop with a gap, if the

speed was just right so gravity was just the

right amount of centripetal force.

GAP

Centrifugal Force

Insect inside a can rotating in a circle

- When a centripetal force acts on an object, it

appears to the object that there is an outward

force. Call this apparent force the centrifugal

force.

What we see

What the insect feels

Demo Bucket Overhead

Centrifugal Force

- Can put a bucket full of water over my head

without getting wet by rotating it fast enough. - Forces exerted on the water by gravity plus

support force of the bucket are centripetal. - Apparent centrifugal force presses the water into

the bucket.

Centripetal Force

Demo Bucket Overhead

- Throw a bowling ball or ball of water overhead.
- As long as the speed is fast enough it will sail

overhead in a curved path. - Gravity by itself supplies the centripetal force.

Gravity

Simulated Gravity

- Centrifugal force could be used to simulate

gravity in a space station. - With the right rate of rotation a person on the

outer rim would feel as if they stood on the

surface of Earth. - Scientifically accurate in the movie 2001 A

Space Odyssey (1968)

Rotation

Demo Spin Out

- Everyday examples of enhanced gravity
- Salad spinner.
- Spin cycle in washer.
- Centrifuge.

Angular Momentum

- There are two types of momentum
- (Linear Momentum) (Mass) x (Velocity)
- and
- (Angular Momentum)
- (Rotational Inertia) x (Rotational Velocity)
- Principle of conservation for both types.

Demo Skaters Spin

- By moving their outstretched arms and legs inward

an ice skater can decrease their bodys

rotational inertia. - By conservation of angular momentum, they

increase their angular velocity (spin faster)

Demo Skaters Spin

LARGE Inertia

Small Inertia

FAST Rotation

Slow Rotation

Angular momentum is constant since (Rotational

Inertia) x (Angular Velocity) remains constant.

Demo Flip the Wheel

Counter- Clockwise Rotation

Clockwise Rotation

Counter- Clockwise Rotation

Demo Spin Up

Counter- Clockwise Rotation

Zero Rotation

Clockwise Rotation

Helicopters Tail

When a helicopters blades start turning in one

direction, by conservation of angular momentum

the body would spin in the opposite

direction. To compensate, the small rotor in the

tail exerts a torque to balance.

Blades

Body

Demo Mid-Air Twist

- Stand up and clear space around you.
- When I say Jump!, jump.
- In mid-air Ill point left or right and I want

you to try to turn so you land facing that

direction.

Jump! Turn Land

How can you rotate in mid-air without pushing off

of anything?

Demo Mid-Air Twist

As you turn your legs 90 degrees, your arms and

torso rotate in the opposite direction. Sticking

your arms out as you turn helps by increasing the

rotational inertia of your upper body. A large

rotation of your legs is exactly cancelled by a

small rotation of your outspread arms and torso.

Your rotation stops as soon as you stop

rotating your upper body but by that time youve

landed with your feet turned to the side. Once on

the ground you can push off on the ground to

restore your arms and torso to a normal stance.

Jump! Turn Land