4-sep-15 physics 1 (garcia) sjsu chapter 8 rotational motion
TRANSCRIPT
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.
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
Circular Motion
Rotational Speed: Revolutions per second
Tangential Speed: Total distance per second
Same Rotational SpeedDifferent Tangential Speeds
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
Bicycles
FAST
SLOW
Notice how gears work on a modern bicycle
Apr 21, 2023 Physics 1 (Garcia) SJSU
Simple & Complex Objects
Motion of simple objects: Position
Motion of complex objects: Position & Rotation
SIMPLE COMPLEX
Axis ofRotation
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
Demo: Hammer Balance
When is the hammer easier to balance on your finger?
BA
Apr 21, 2023 Physics 1 (Garcia) SJSU
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?
Apr 21, 2023 Physics 1 (Garcia) SJSU
Demo: Long Legs
Long legs have greater rotational inertia than short legs so long legged animals have a slow walking stride.
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
Demo: Hoop & Disk Racing
Roll a hoop and a disk down a ramp; which wins the race?
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
Lever Arm
Lever arm is perpendicular distance from axis of rotation to the direction of the force.
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
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Check Yourself
In which case are you exerting more torque?
A
BLever ArmLever Arm
almost zero
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
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.
Apr 21, 2023 Physics 1 (Garcia) SJSU
Locating Center of Gravity
Balance an object to find center of gravity
Centerof
Gravity
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
Stability
Object is stable if CG is above the base.
CG CG
Wei
ght
Wei
ght
BASEAxis
AxisBASE
STABLE
UNSTABLE
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
Demo: Balanced Bird
Where is the bird’s center of gravity?
Apr 21, 2023 Physics 1 (Garcia) SJSU
Demo: Mystery Wheel
Wheel doesn’t roll down hill. How is that possible?
Apr 21, 2023 Physics 1 (Garcia) SJSU
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.
Apr 21, 2023 Physics 1 (Garcia) SJSU
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?
Apr 21, 2023 Physics 1 (Garcia) SJSU
Centripetal Force Examples
Friction force (tires) is centripetal.
Tension force (string) is centripetal.
Gravity force (on satellite due to Earth) is centripetal
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
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Magnitude of Centripetal Force
Magnitude of centripetal force is large when
• Speed is large• Radius is small• Mass is large
Apr 21, 2023 Physics 1 (Garcia) SJSU
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.
Apr 21, 2023 Physics 1 (Garcia) SJSU
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.
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
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.
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
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
Apr 21, 2023 Physics 1 (Garcia) SJSU
Demo: Spin Out
Everyday examples of “enhanced” gravity:
Salad spinner.
Spin cycle in washer.
Centrifuge.
Apr 21, 2023 Physics 1 (Garcia) SJSU
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.
Apr 21, 2023 Physics 1 (Garcia) SJSU
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)
Apr 21, 2023 Physics 1 (Garcia) SJSU
Demo: Skater’s Spin
SlowRotation
FASTRotation
LARGE Inertia Small Inertia
Angular momentum is constant since(Rotational Inertia) x (Angular Velocity) remains constant.
Apr 21, 2023 Physics 1 (Garcia) SJSU
Demo: Flip the Wheel
Counter-ClockwiseRotation
Counter-ClockwiseRotation
ClockwiseRotation
Similar tocollisions
Apr 21, 2023 Physics 1 (Garcia) SJSU
Demo: Spin Up
ZeroRotation
ClockwiseRotation
Counter-ClockwiseRotation
Similar torecoil
Apr 21, 2023 Physics 1 (Garcia) SJSU
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.