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Causes of Circular Motion

Causes of Circular Motion. Chapter 7, Section 2 & 3 Pg. 253-265. v t. v t. v t. Tangential Speed. Tangential Speed (v t ) is the instantaneous linear speed of an object at any point in its circular path. radius. angular speed. How do we calculate the tangential speed?. Vt = r ω.

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Causes of Circular Motion

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  1. Causes of Circular Motion Chapter 7, Section 2 & 3 Pg. 253-265

  2. vt vt vt Tangential Speed Tangential Speed (vt)is the instantaneous linear speed of an object at any point in its circular path.

  3. radius angular speed How do we calculate the tangential speed? Vt = rω Tangential Speed

  4. Vt = 1.88 m/s r = 0.06 m Sample Problem The radius of a CD in a computer is 0.06 m. If a microbe riding on the disc’s rim has a tangential speed of 1.88 m/s what is the disc’s angular speed? Vt = rω ω = Vt/r I’m getting dizzy!!! ω = (1.88 m/s)/ (0.06 m) ω = 31.3 rad/s

  5. at Tangential Acceleration Tangential acceleration (at)is the instantaneous linear acceleration of an object at any point in its circular path.

  6. How do we calculate the tangential acceleration? Tangential Speed: Vt = rω Acceleration measures the change in speed over a given amount of time. at = Vt/Δt = rΔω/Δt Angular acceleration: α = Δω/Δt at = rα

  7. at = 3.3 m/s² r = ? α = 0.50 rad/s² Sample Problem A spinning ride at a carnival has an angular acceleration of 0.50 rad/s². How far is a rider from the center of the ride if his tangential acceleration is 3.3 m/s²? at = rα r = at/α r = (3.3 m/s²) / (0.50 rad/s²) r = 6.6 m

  8. at ac Centripetal Acceleration Centripetal acceleration (ac)is the acceleration that is directed towards the center of a circular path.

  9. Calculating Centripital Acceleration ac = vt²/r or Since Vt = rω ac = (rω)²/r ac = rω²

  10. vt= ? r = 48.2 m ac = 8.05 m/s² vt = √(ac)(r) = √ (8.05 m/s²) (48.2 m) Sample Problem What is the tangential speed of a test car moving at a constant speed around a circular track that is 48.2 m from the track’s center and has a centripetal acceleration of 8.05 m/s²? ac = vt²/r vt² = (ac)(r) vt = 19.7 m/s

  11. at and vt ac Forces that maintain circular motion What is causing an object to move in a circular motion? Centripetal acceleration is only part of the answer! What causes ac to occur in the first place?

  12. vt and at Fc at and vt ANSWER = CENTRIPETAL FORCE!!! Any object that experiences a circular motion has a force directed towards its center axis (Fc).

  13. Centripetal force can be defined as: Fc = mac Since ac = vt²/r = rω² Fc = mvt²/r Fc = mrω²

  14. Sample Problem vt = 30 m/s r = 100.0 m A pilot is flying a small plane at 30 m/s in a circular path with a radius of 100.0 m. If a force of 635 N is needed to maintain the pilot’s circular motion, what is the pilot’s mass? Fc = mvt²/r Fc = 635 N m = Fc(r)/vt² m = (635 N)(100.0 m)/ (30 m/s)² m = 70.6 kg

  15. Homework Assignment • Practice: Pg. 255 # 2 Pg. 256 # 1 Pg. 258 # 1, 4 Pg. 261 # 1,3 Pre-AP: Pg. 270 # 18 & 20

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