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Uniform Circular Motion

Uniform Circular Motion. V t. r. ω. V t. Linking… Linear Motion to Uniform Circular Motion. Linking… Linear Motion to Uniform Circular Motion. Uniform Circular Motion. ( Δθ ) Angular Displacement is difference between the final and initial angles. Unit rad

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Uniform Circular Motion

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  1. Uniform Circular Motion Vt r ω Vt

  2. Linking… Linear Motion to Uniform Circular Motion

  3. Linking… Linear Motion to Uniform Circular Motion

  4. Uniform Circular Motion • (Δθ) Angular Displacement is difference between the final and initial angles. Unit rad • (s) Arc Length the distance around the arc of Δθ. Partial circumference. Unit meter • (r) Radius a straight line from the center to the circumference of a circle or sphere.Unit meter • (rad) Radian is a angular unit of measurement and is essential to the understanding of rotational motion. • 1 rev = 360˚;1 rad = 57.2957º ; • one rev = 2πrad Be sure to change the mode of your calculator to radians

  5. Uniform Circular Motion • (T) Period time of one revolution. Unit sec • (f)Frequency is the number of revolutions per second. Unit Sec -1 or Hz • (ω)Angular Velocity the rate of change of angular displacement. unit rad/sec • (vt) Tangential Velocity the linear velocity of something moving in a circular path • (α) Angular Acceleration the rate of change in angular velocity. unit rad/sec2

  6. Uniform Circular Motion • (ac) Centripetal Acceleration the rate of change of constant velocity. Suppose we had a circle with angle, q, between 2 radaii. You may recall: Dv v v vo q vo Centripetal means “center seeking” so that means that the acceleration points towards the CENTER of the circle

  7. Circular Motion and N.S.L Recall that according to Newton’s Second Law, the acceleration is directly proportional to the Force. If this is true: Since the acceleration and the force are directly related, the force must ALSO point towards the center. This is called CENTRIPETAL FORCE. NOTE: The centripetal force is a NET FORCE. It could be represented by one or more forces. So NEVER draw it in an F.B.D.

  8. Labeling

  9. Angular Speed vs Tangential Speed Compare both types Tangential Speed Angular Speed • Tangential Velocity (Vt) • The linear speed of something moving in a circular path. • Change in displacement per unit time. • Angular Speed (ω) • Is the number of rotations per unit of time. • Change in angular displacement per unit time. B, being farther from the center travels a longer path and has a greater tangential speed than A. Tangential velocity of an object is linearly proportional to the distance from the center. Increase in the distance results in the increase in the amount of speed. Unlike tangential velocity, angular speed of all points on the platform doing circular motion are equal to each other since the number of rotations per unit time are equal. Both A and B have the same angular displacement, therefore they have the same angular speed.

  10. Tangential Velocity Demo

  11. Examples The blade of a windshield wiper moves through an angle of 90 degrees in 0.28 seconds. The tip of the blade moves on the arc of a circle that has a radius of 0.76m. What is the magnitude of the centripetal acceleration of the tip of the blade?

  12. Examples A 150-g ball at the end of a string is revolving uniformly in a horizontal circle of radius 0.600 m. The ball makes 2.00 revolutions in a second. What is its centripetal acceleration? Not exactly right!

  13. Examples What is the minimum coefficient of static friction necessary to allow a penny to rotate along a 33 1/3 rpm record (diameter= 0.300 m), when the penny is placed at the outer edge of the record? Top view FN Ff mg Side view

  14. Examples Fg Venus rotates slowly about its axis, the period being 243 days. The mass of Venus is 4.87 x 1024 kg. Determine the radius for a synchronous satellite in orbit around Venus. (assume circular orbit) 1.54x109 m

  15. Examples mg T The maximum tension that a 0.50 m string can tolerate is 14 N. A 0.25-kg ball attached to this string is being whirled in a vertical circle. What is the maximum speed the ball can have (a) the top of the circle, (b)at the bottom of the circle?

  16. Examples At the bottom? T mg

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