Rotational Motion and the Law of Gravity 7.1 Measuring Rotational Motion.
Rotational Motion
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Transcript of Rotational Motion
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Rotational Motion
Rotation of rigid objects- object with definite shape
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Rotational Motion
• All points on object move in circles
• Center of these circles is a line=axis of rotation
• What are some examples of rotational motion?
• What is the difference between rotation and revolution?
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Speed
• Rotating objects have 2 speeds:
• Linear speed (also known as tangential)
• Rotational speed
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Linear Speed
• Imagine yourself on a merry-go-round. At any moment, describe the direction of your linear speed
• Who goes faster- A or B?
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Velocity:Linear vs Angular
• Each point on rotating object also has linear velocity and acceleration
• Direction of linear velocity is tangent to circle at that point
• “the hammer throw”
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Angular Velocity
• Angular velocity rate of change of angular position
• measured in revolutions/time
Thus RPM= revolutions per minute
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Angular Velocity
• All points in rigid object rotate with same angular velocity (move through same angle in same amount of time)
• Related to linear- if you speed up the rotation, both linear and angular velocity increases
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Velocity:Linear vs Angular
• Even though angular velocity is same for any point, linear velocity depends on how far away from axis of rotation
• Think of a merry-go-round
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So how are they related?
• The farther out you are, the faster your linear speed
• So linear velocity increases with your radius
• The faster your angular speed, the faster your linear speed
• So linear velocity increases with angular velocity
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Centripetal Acceleration
• If object is moving in a circle, its direction is constantly changing towards the center so the acceleration must be in that direction
• Then why when you turn a corner in a car do you feel pushed out, not in?
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Centripetal Acceleration
• acceleration= change in velocity (speed and direction) in circular motion you are always changing direction- acceleration is towards the axis of rotation
• The farther away you are from the axis of rotation, the greater the centripetal acceleration
• Demo- crack the whip• http://www.glenbrook.k12.il.us/gbssci/phys/
mmedia/circmot/ucm.gif
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Centripetal examples
• Wet towel
• Bucket of water
• Beware….inertia is often misinterpreted as a force.
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The “f” word• When you turn quickly- say in a car or roller
coaster- you experience that feeling of leaning outward
• You’ve heard it described before as centrifugal force
• Arghh……the “f” word• When you are in circular motion, the force is
inward- towards the axis= centripetal• So why does it feel like you are pushed
out???INERTIA
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Centripetal acceleration and force
• Centripetal acceleration– Towards axis of rotation
• Centripetal force– Towards axis of rotation
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Frequency
• Frequency= f= revolutions per second (Hz)
• Period=T=time to make one complete revolution
• T= 1/f
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Frequency and Period example
• After closing a deal with a client, Kent leans back in his swivel chair and spins around with a frequency of 0.5Hz. What is Kent’s period of spin?
T=1/f=1/0.5Hz=2s
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Rolling
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Rolling
• Rolling= rotation + translation
• Static friction between rolling object and ground (point of contact is momentarily at rest so static)
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Inertia
• Remember our friend, Newton?
• F=ma• In circular motion:
– torque takes the place of force
– Angular acceleration takes the place of acceleration
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Rotational Inertia=LAZINESS
• Moment of inertia for a point object
I = Resistance to rotation• I plays the same role for rotational motion as
mass does for translational motion• I depends on distribution of mass with respect
to axis of rotation• When mass is concentrated close to axis
of rotation, I is lower so easier to start and stop rotation
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Rotational InertiaUnlike translational motion, distribution of mass
is important in rotational motion.
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Rotational inertia- baseball
• A long bat that you hold at the end has a lot of rotational inertia- mass is far away from the axis of rotation
• Thus it is hard to get moving
• Younger players “choke up” on the bat by moving their hands towards the middle- this makes the bat have less rotational inertia- it’s easier to swing
• Try the rotating sticks!
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Changing rotational inertia
• When you change your rotational inertia you can drastically change your velocity
• So what about conservation of momentum?
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Angular momentum
• Momentum is conserved when no outside forces are acting
• In rotation- this means if no outside torques are acting
• A spinning ice skater pulls in her arms (decreasing her radius of spin) and spins faster yet her momentum is conserved
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Torque
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How do you make an object start to rotate?
Pick an object in the room and list all the ways you can think of to
make it start rotating.
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Torque
• Let’s say we want to spin a can on the table. A force is required.
• One way to start rotation is to wind a string around outer edge of can and then pull.
• Where is the force acting?
• In which direction is the force acting?
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Torque
Force acting on outside of can. Where string leaves the can, pulling tangent.
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Torque
• Where you apply the force is important.• Think of trying to open a heavy door- if
you push right next to the hinges (axis of rotation) it is very hard to move. If you push far from the hinges it is easier to move.
• Distance from axis of rotation =lever arm or moment arm
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Torque
• Which string will open the door the easiest?
• In which direction do you need to pull the string to make the door open easiest?
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Torque
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Torque• tau = torque (mN)• If force is perpendicular, =rF• If force is not perpendicular, need to find the
perpendicular component of F
=rF
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Torque example (perpendicular)
• Ned tightens a bolt in his car engine by exerting 12N of force on his wrench at a distance of 0.40m from the fulcrum. How much torque must he produce to turn the bolt? (force is applied perpendicular to rotation)
Torque= =rF=(12N)(0.4m)=4.8mN
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More than one Torque
• When 1 torque acting, angular acceleration is proportional to net torque
• If forces acting to rotate object in same direction net torque=sum of torques
• If forces acting to rotate object in opposite directions net torque=difference of torques
• Counterclockwise +• Clockwise -
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Multiple Torque experiment
• Tape a penny to each side of your pencil and then balance pencil on your finger.
• Each penny exerts a torque that is equal to its weight (force of gravity) times the distance r from the balance point on your finger.
• Torques are equal but opposite in direction so net torque=0
• If you placed 2 pennies on one side, where could you place the single penny on the other side to balance the torques?
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Torque and center of mass
• Stand with your heels against the wall and try to touch your toes.
• If there is no base of support under your center of mass you will topple over
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Center of mass
• The average position of all the mass of an object
• If object is symmetrical- center of mass is at the center of the object
• Where is the center of mass of a meter stick?• A donut?• How could you find the center of mass of an
object?
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Torque and football
• If you kick the ball at the center of mass it will not spin
• If you kick the ball above or below the center of mass it will spin