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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 Angular Speed Circular Speed**

ω (lower case Omega Ω)

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

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**Describe Earth’s motion using the words rotate, revolve, and axis.**

Axis: Straight line around which rotation takes place. Days on Earth. Rotation: Spin. Axis is located within the object. Days on Earth. Revolution: Object turns about an external axis. Earth years.

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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 Questions: Challenges:**

1) How is radius related to revolution speed? 2) What happens when you are spinning the stopper at a constant rate and then suddenly pull down on the string? Why does this happen? 3) Does a spinning object accelerate? If so, what is the direction of acceleration? Challenges: 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.

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Tangential Speed

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**How 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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**How 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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What happens when you are spinning the stopper at a constant rate and then suddenly pull down on the string? Why 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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**what is the direction of acceleration of an object in uniform circular motion?**

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 Fc 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. Centripetal means “center-seeking” Always acts inwards

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**Centripetal Acceleration ac**

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. radius of curve is 50m speed of cars- 13.4m/s What should the angle of the bank be?

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The banked ramp exit FN FNy FNx Fg

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**How long will it take to land?**

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? 750m 375m 105m 210m 150m c) 105m**

v0x=15m/s h=250m R What is the range R? 750m 375m 105m 210m 150m c) 105m

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**What is the speed of the object when it hits the ground?**

Review Problems v0x=15m/s h=250m R What is the speed of the object when it hits the ground? 72m/s 15m/s 150m/s 70m/s 21m/s a) 72m/s

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Review Problems A (peak) v0 What is the direction of the acceleration vector and velocity vector at point A? 0m/s2 and 0m/s d) a v a v e) a m/s 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 student’s centripetal acceleration? Normal Force d) Centrifugal Force Weight e) None 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 (ah/at)? 2/1 1/2 1 2^(1/2) 2^-(1/2) b)

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

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

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

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**Review Problems We need an equation with T in it! What is r?**

θ We need an equation with T in it! r What is 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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Review Problems L θ r

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