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Circular Motion 2D Forces and Motion

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Which is faster? The horse on the outside or the horse on the inside?

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Merry-Go-Round Same rotational speed for all animals on the Merry-Go-Round because they are attached rigidly. Animals further out have a greater linear speed.

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Rotational Speed Also called Also called Angular Speed Angular Speed Circular Speed Circular Speed ω (lower case Omega Ω) ω (lower case Omega Ω)

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Linear Speed (v) Also called Also called Tangential Speed Tangential Speed v or v T v or v T

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Describe Earths motion using the words rotate, revolve, and axis. Rotation: Spin. Axis is located within the object. Days on Earth. Revolution: Object turns about an external axis. Earth years. Axis: Straight line around which rotation takes place. Days on Earth.

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Frequency vs. Period Period (T)- The time it takes for one full rotation or revolution of an object in seconds. Frequency (f)- The number or rotations or revolutions per unit time, measured in Hertz (Hz)

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Revolution Lab Q UESTIONS : Q UESTIONS : 1) H OW IS RADIUS RELATED TO REVOLUTION SPEED ? 1) H OW IS RADIUS RELATED TO REVOLUTION SPEED ? 2) W HAT HAPPENS WHEN YOU ARE SPINNING THE STOPPER AT A CONSTANT RATE AND THEN SUDDENLY PULL DOWN ON THE STRING ? W HY DOES THIS HAPPEN ? 2) W HAT HAPPENS WHEN YOU ARE SPINNING THE STOPPER AT A CONSTANT RATE AND THEN SUDDENLY PULL DOWN ON THE STRING ? W HY DOES THIS HAPPEN ? 3) D OES A SPINNING OBJECT ACCELERATE ? I F SO, WHAT IS THE DIRECTION OF ACCELERATION ? 3) D OES A SPINNING OBJECT ACCELERATE ? I F SO, WHAT IS THE DIRECTION OF ACCELERATION ? C HALLENGES : C HALLENGES : 1) Spin a rubber stopper above your head at several different lengths to answer the question above. Do multiple trials. 1) Spin a rubber stopper above your head at several different lengths to answer the question above. Do multiple trials. 2) Graph your data to help find the mathematical relationship between radius and revolution speed. 2) Graph your data to help find the mathematical relationship between radius and revolution speed.

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Tangential Speed

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H OW IS RADIUS RELATED TO REVOLUTION SPEED ? In Uniform Circular Motion (fixed tangential speed), a larger radius will result in a smaller rotational speed.

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H OW IS RADIUS RELATED TO REVOLUTION SPEED ? In Uniform Circular Motion (fixed tangential speed), a larger radius will result in a smaller rotational speed.

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Rotational Speed

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W HAT HAPPENS WHEN YOU ARE SPINNING THE STOPPER AT A CONSTANT RATE AND THEN SUDDENLY PULL DOWN ON THE STRING ? W HY DOES THIS HAPPEN ? It spirals in because you apply a constant force inward. You reduce the radius.

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WHAT IS THE DIRECTION OF ACCELERATION OF AN OBJECT IN UNIFORM CIRCULAR MOTION ?

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There is a radial component of acceleration responsible for the constant direction change, and a tangential component of acceleration which results in an increase or decrease in tangential speed.

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Describe the path of the stopper IF you were to cut the string between the tube and the bottom weight

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Centripetal Force F c A force of some kind is required to maintain circular motion. Why? A force of some kind is required to maintain circular motion. Why? Any force that causes an object to follow a circular path is called a centripetal force. Any force that causes an object to follow a circular path is called a centripetal force. Centripetal means center-seeking Centripetal means center-seeking Always acts inwards Always acts inwards

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Centripetal Acceleration a c Tangential Velocity Radius

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Centripetal Force

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The banked ramp exit The goal is to design a banked ramp exit that drivers can round safely even on ice. The goal is to design a banked ramp exit that drivers can round safely even on ice. radius of curve is 50m radius of curve is 50m speed of cars- 13.4m/s speed of cars- 13.4m/s What should the angle of the bank be? What should the angle of the bank be?

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The banked ramp exit FgFg FNFN F Ny F Nx

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Review Problems Derive the expression (fully simplified) that will determine the time it will take for a projectile launched on flat ground to reach its maximum height. How long will it take to land?

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Review Problems What is the range R? a)750m b)375m c)105m d)210m e)150m What is the range R? a)750m b)375m c)105m d)210m e)150m v 0x =15m/s h=250m R c) 105m

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Review Problems What is the speed of the object when it hits the ground? a)72m/s b)15m/s c)150m/s d)70m/s e)21m/s What is the speed of the object when it hits the ground? a)72m/s b)15m/s c)150m/s d)70m/s e)21m/s v 0x =15m/s h=250m R a) 72m/s

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Review Problems v0v0 A (peak) What is the direction of the acceleration vector and velocity vector at point A? a)0m/s 2 and 0m/s d) a v b) a ve) a 0m/s c) a v What is the direction of the acceleration vector and velocity vector at point A? a)0m/s 2 and 0m/s d) a v b) a ve) a 0m/s c) a v c)

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Review Problems A very agile physics student is standing on one of those spinny things in a playground without slipping. Which force provides the students centripetal acceleration? a)Normal Forced) Centrifugal Force b) Weighte) None c) Friction on shoes f) Abnormal force A very agile physics student is standing on one of those spinny things in a playground without slipping. Which force provides the students centripetal acceleration? a)Normal Forced) Centrifugal Force b) Weighte) None c) Friction on shoes f) Abnormal force c)

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Review Problems Two quarters are on a spinning turntable. One head side up and one tail side up. Heads is at a distance R/2 from the center. Tails is a distance R from the center. What is the ratio of accelerations (a h /a t )? a) 2/1 b)1/2 c) 1 d)2^(1/2) e)2^-(1/2) Two quarters are on a spinning turntable. One head side up and one tail side up. Heads is at a distance R/2 from the center. Tails is a distance R from the center. What is the ratio of accelerations (a h /a t )? a) 2/1 b)1/2 c) 1 d)2^(1/2) e)2^-(1/2) b)

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Review Problems A B C A B (along rope) C D (tangent to curve) E For the pendulum on the left, which vector on the right possibly shows the direction of acceleration at point A? C C

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Review Problems A B C A B C D E For the pendulum on the left, which vector on the right shows the direction of acceleration at point B? A A

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Review Problems For the conical pendulum above, find a fully simplified expression for the period in terms of theta, L, g, and other constants. L θ

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Review Problems L θ We need an equation with T in it! What is r? r Ok, so what is v? Take it easy, make an FBD.

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Review Problems L θ r

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L θ r

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