rotational mechanics rotational motion rotational speed or angular speed typically measured in...
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Rotational Motion Rotational Speed or Angular Speed Typically measured in rpm’s or degrees/sec, but the SI unit is radians/sec ω = Δ Θ / Time ??? What is the rotational speed of a clock’s “second” hand in rpms? Angular Acceleration: The rate of change in Angular speed α = Δ ω / TimeTRANSCRIPT
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Rotational Mechanics
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Rotational Motion
Rotational Speed or Angular SpeedTypically measured in rpm’s or degrees/sec, but the SI unit is radians/sec
ω = Δ Θ / Time
??? What is the rotational speed of a clock’s “second” hand in rpms?
Angular Acceleration:The rate of change in Angular speed
α = Δ ω / Time
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Rotational Motion VS Linear MotionThe linear speed or tangential speed of an object
depends on its radial distance. v = ω r
Ex: The horses on a carousel all go around with the same angular speed, but the outside horses have a greater linear
speed.
??? Suppose two cars have a race. Car A has 12 inch wheels that can rotate at 500 rpm. Car B has 24 inch wheels that can rotate at 400 rpm. Which car will win the race?
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Measuring Angular Speed1. Record the time it takes an object to roll down
an incline 1 meter long.2. Determine the diameter and circumference of the
object.3. Determine the number of rotations the object
went through when it rolled 1 meter.4. Determine the object’s average Angular Speed.
(rotations/sec)5. Determine the object’s final Angular Speed.
(rotations/sec)6. Determine the object’s angular acceleration.
(rotations/sec2)7. What are some possible reasons why different
objects rolled down at different rates?
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Rotation ReviewA wheel starts at rest and then rolls 5
times down a hill in just 3 seconds.
1. What was its average angular speed in rotations/sec?
2. What was its final angular speed in rotations/sec?
3. What was its angular acceleration?
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Buttered Cat Paradox
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Warm-up
1. Where is the most exciting place to sit on a merry-go-round? Why?
2. If railroad wheels are on the same axle (same angular speed), how is it possible for trains to turn?
3. What should roll down a hill faster, a solid sphere, solid disk or hollow hoop (assume same mass)?
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Rotational InertiaIntroduction• Observe the motion of a Ball, Solid Disk, and a
Hoop rolling down an incline.• Rotate the two different “inertia sticks”• Observe the falling chimney.Definition:
Rotational Inertia directly depends on the mass of a rotating object and on how far the mass is located from the axis of rotation.
Other Examples:Tight rope walkers, FlyWheels,Running, Gymnasts
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More rotation examples
Ex. If you turn off your workshop grinder and electric drill at the same time, which one takes longer to come to a stop? (2 reasons)
Ex. Why are little kids told to “choke up” on a baseball bat?
Ex. Why do the front brakes wear out faster than the rear brakes on a car?
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Torque• Torques cause changes in rotation! Just as
Forces cause accelerations.• Torque = (Force) x (lever arm distance)
– Ex: 100 Newtons of force is applied perpendicularly to a 0.5 meter wrench.
– Remember: the perpendicular component of the applied force is what counts!
– Ex: Torque Feeler, Torque wrench, Cheater Bar?
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Torque examplesMeter stick challenge (weighted and
unweighted)HammerSee-sawScrewdriver—how would you modify the
shape to maximize torque?
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Center of Mass / Center of GravityCenter of Mass (Gravity) is the average position of all the mass
(weight) that comprises an object (balance point). Ex: Where is the CM of a ball located?
Ex: Where is the CM of a hollow disc located?Ex: Where is the CM of a hammer located?
For freely rotating objects; they will rotate around their CM.Baton twirling, riflesBaby in-uteroEarth-moon system—why does the Earth wobble?
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Earth/Moon Sun/Earth
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Stability• An object is stable if the sum of the torques
acting on it equal zero (cancel each other out)– Ex: A 2 kg mass is suspended from the 10
cm mark of a meter stick. Where can a 5 kg mass be placed on the meter stick so that it is balanced about the 50 cm mark?
• You can also consider objects to be stable if their CM is located directly above or beneath an area of support.• Ex: Tower of Pisa, Heel/Toes against the
wall, Chair/Head/Wall pick up• Freshmen! Pregnant women!
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Stability – Check Questions1. What is the torque caused by a 250 N
force applied at the end of a 40 cm wrench?
2. A 5 kg mass is suspended from the 5 cm mark of a meter stick. Where can a 8 kg mass be placed on the meter stick so that it is balanced about the 50 cm mark?
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Centripetal Force and Acceleration• Centripetal Force is a force exerted on an object that
causes it to change direction. It is always directed towards the center of curvature.– ac = v2/r– Fc = mv2/r
– Centrifugal Force is the reaction force.– Ex: A 0.1 kg ball twirled around by a string at a
constant 5 m/s.– What is the centripetal acceleration?– What is the centripetal force on it?– Distinguish the centripetal force from the
centrifugal force.
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What On Earth is Spin?
http://www.youtube.com/watch?v=H4JUTnkiGpI&edufilter=8gyTAQpnAaFWN9xxR7pk4A&safe=active
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Simulated Gravity
By rotating a space station, inhabitants will be forced to move in a circular path and experience a centripetal force – much like gravity.
However the space station will most likely be large to overcome dizzying effects and varying amounts of Centripetal ForceEx’s: 2001, 2010, Mission Mars, Armageddon
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Review
1. What is the weight of the above meter stick shown above?
2. What is the centripetal acceleration of a space station that is 20 meters in radius and rotating at 10 m/s?
10 N
20 cm0 cm 100 cm
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Angular Momentum Conservation
• Angular Momentum is Rotational Inertia IN MOTION!– L = I
• Conservation of Angular Momentum:– In the absence of net torque, the total
angular momentum of a system is conserved.
• Ex’s– Spinning stool and tire, Ice Skater,
Gymnast, Earth’s rotation, Comets in orbit. Helicopters…
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XKCD fans?
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What allows cats to flip over and ALWAYS land on their feet?!?
(video)
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Helicopters
Tail Rotor prevents the helicopter from
spinning out of control.
Why don’t these have tail rotors?
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Precession• If there is an outside torque acting on a
system, then the angular momentum will change.
• Ex: Hanging bike tire, Earth’s precession (~26,000 yrs), Spinning Top