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Circular Motion

Circular Motion. Circular Motion. Can an object accelerate if its speed remains constant? Yes, b/c velocity is a vector quantity; just as any change in speed means that there is a change in velocity, so too does a change in direction indicate a change in velocity. Rotation & Revolution.

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Circular Motion

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  1. Circular Motion

  2. Circular Motion • Can an object accelerate if its speed remains constant? • Yes, b/c velocity is a vector quantity; just as any change in speed means that there is a change in velocity, so too does a change in direction indicate a change in velocity.

  3. Rotation & Revolution • Axis – straight line around which rotation takes place • Rotation – the spinning motion that takes place when an object rotates about its own axis (ballerina, ice dancer, etc…) • Revolution – Motion of an object turning around an axis outside the object. (marker on the record, you on the earth, etc…)

  4. The Earth • What does the earth do, revolve or rotate? • BOTH!! • It revolves around the sun • It rotates about its axis (north-south pole axis)

  5. Radians, AAAahhh!! • What is a radian? • It is when the arc on the outside of a circle is equal in length to the circle’s radius • A Useful Conversion 1 rev. = 2π(rad) = 360 ˚

  6. From degrees to radians Convert the following into radians • 35 ˚ • 175 ˚ • 235 ˚ • 360 ˚ • 465 ˚ • 520 ˚ • 720 ˚ Take 5 & Solve!!

  7. From degrees to radians Convert the following into radians • 35 ˚ = 0.61 rad • 175 ˚ = 3.05 rad • 235 ˚ = 4.10 rad • 360 ˚ = 6.28 rad • 465 ˚ = 8.12 rad • 520 ˚ = 9.08 rad • 720 ˚ = 12.57 rad ‘s

  8. Radians and Arc Length Lab • Radians and Arc Length Lab • Students will be able to develop the relationship between radian and arc length • Students will be able to demonstrate and explain why there are 2π radians in one full revolution. PROVE IT!! - LAB TIME!!!!

  9. Lab Time!

  10. The Speeds? • Linear Speed – is simply distance covered divided by time. It is what we have called “speed” v = distance / time • Angular Speed – is simply the angle covered divided by time. It is the number of rotations per unit of time. ω = Number of Radians / time (Record Demo)

  11. Angular Speed Question: • On a merry-go-round, where would you be moving with the greatest linear speed? Rotational Speed? Answer: • Outside • Anywhere

  12. Angular Speed (ω ) How to Measure Angular Speed: To calculate the angular speed angle (in radians) and the time for one revolution ω = 2π(rad) / T The time for an object to make one revolution is called the period (T)

  13. From Angular speed to Linear • To calculate the linear speed of an object in circular motion we need to know the angular speed and the radius. • Together: • V = ωr • Angular velocity x radial distance • The further you are from the center of a rotating platform, the greater your linear velocity.

  14. Angular Velocity Sample Problems *solve using radians / second

  15. Solutions • 1 revolution: (2π) / 4.56 s = 1.38 rad/s • 1 revolution: (2π)/ 24 hr (86,400 s) = 7.3 x 10-5 rad/s • 3.25 revolutions: 3.25(2π) / 1 s = 20.4 rad/s • 45 revolutions = 282.7 rad 282.7 rad / 60 s = 4.7 rad/s

  16. So, What is the Linear speed V = ω r • Merry Go Round: 1.38 rad/s x 8.5 m = 11.73 m/s • Earth: 7.3 x 10-5 rad/s x (6.38 x 106m) = 463.7 m/s!!! That means 1038 mph!! *Earth radius is 6.38 x 106m *This means you are going 463.7 m/s… right now!!!

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