4-Sep-15 Physics 1 (Garcia) SJSU Chapter 8 Rotational Motion.

Apr 21, 2023 Physics 1 (Garcia) SJSU

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)

We’ve 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.

Axis

Radius

Diameter

Axis

RadiusDiameter


Circular Motion

Rotational Speed: Revolutions per second

Tangential Speed: Total distance per second

Same Rotational SpeedDifferent 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?

12


Bicycles

FAST

SLOW

Notice how gears work on a modern bicycle


Simple & Complex Objects

Motion of simple objects: Position

Motion of complex objects: Position & Rotation

SIMPLE COMPLEX

Axis ofRotation


Mass is a measure of inertia for linear motion.

Rotational inertia is similar concept for rotation.

Inertia

M m

Gold brick Normal brick

Difficult to move Easy to move

x x

Wood Bat Plastic Pee-wee Bat

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

Easyto

Rotate

Hardto

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?

BA


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?

Winner


Demo: Hoop & Disk Racing

Roll a hoop and a disk down a ramp; which wins the race?


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)

Torque


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.

ForceForce

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 onFloor

ReactionForce

LeverArm

Feet apart Feet together


Check Yourself

In which case are you exerting more torque?

A

BLever ArmLever Arm

almost zero


Balance of TorquesTorques clockwise and counter-clockwise

balance in both cases since

(250 N) x (3 m) = (500 N) x (1.5 m)

Her lever armis 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

Centerof

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.

x CG

PEPSI


Stability

Object is stable if CG is above the base.

CG CG

Wei

ght

Wei

ght

BASEAxis

AxisBASE

STABLE

UNSTABLE


Check Yourself

Three trucks

are parked on

a slope. Which

truck(s) tip

over?CG

CG

CG

BASEBASE

Balance & Ballet

On one foot

Feet flat on the floor

Balance is

OK anywhere

in here

Center of Gravitylocated above thedancer’s toe

The force of gravity and the support force of the floor can balance only when a dancer’s center of gravity is located above the base of support.

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 bird’s center of gravity?


Demo: Mystery Wheel

Wheel doesn’t 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

A

B C

D

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

Friction force (tires) is centripetal.

Tension force (string) is centripetal.

Gravity force (on satellite due to Earth) is centripetal


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).

SupportForce


Magnitude of Centripetal Force

Magnitude of centripetal force is large when

• Speed is large• Radius is small• Mass is large


Hurricanes

Rita, 9/22/05

LH

H – High PressureL – Low PressureF – Centripetal Forcedue to pressure difference

F

Hurricane’s strength (wind speed) depends on how low the pressure gets in the center.


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.

Velocity

Release

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.

Velocity

Release

GAP


Centrifugal Force

What we see

What theinsect feels

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.


Demo: Bucket Overhead

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.

CentripetalForce

CentrifugalForce


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: Skater’s Spin

By moving their outstretched arms and legs inward an ice skater can decrease their body’s rotational inertia.

By conservation of angular momentum, they increase their angular velocity (spin faster)


Demo: Skater’s Spin

SlowRotation

FASTRotation

LARGE Inertia Small Inertia

Angular momentum is constant since(Rotational Inertia) x (Angular Velocity) remains constant.


Demo: Flip the Wheel

Counter-ClockwiseRotation


ClockwiseRotation

Similar tocollisions


Demo: Spin Up

ZeroRotation

ClockwiseRotation


Similar torecoil


Blades

Body

Helicopter’s Tail

When a helicopter’s 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.

Demo: Mid-Air Twist

Stand up and clear space around you.

When I say “Jump!”, jump.

In mid-air I’ll 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

Jump! Turn Land

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 you’ve 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.

4-Sep-15 Physics 1 (Garcia) SJSU Chapter 8 Rotational Motion.

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Transcript of 4-Sep-15 Physics 1 (Garcia) SJSU Chapter 8 Rotational Motion.