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Uniform Circular Motion

newman avatar
newman
21 diapositives · 356 Views · Aug 04, 2014

Explore the principles of uniform circular motion, centripetal force, and angular velocity through engaging scenarios. Discover where a ball goes when a string breaks while swinging it in a circle. Learn why centrifugal force is a misconception and delve into centripetal force calculations in various contexts, including planetary motion and satellite dynamics. Unravel the relationships between mass, distance, and gravitational forces, illuminating the mechanics behind orbits and motion in a circular path.

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Uniform Circular Motion
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  1. Uniform Circular Motion

  2. Q: You are swinging a ball around in a circle on a string. Suddenly the string breaks. Where does the ball go? • A) out from the center of the circle • B) in to the center of the circle • C) tangent to the path of the circle • D) it drops to the ground as soon as the string breaks

  3. Centripetal motion • When an object is moving in a circular path, this object is being acted upon by a centripetal force. • Centripetal force: a force that makes a body follow a curved path: it is always directed orthogonal to the velocity of the body

  4. Centrifugal force… • …is fake! • There is no such thing as centrifugal force. • When people talk about centrifugal forces they are talking about the inertial effects of circular motion and the opposing force to the centripetal force that allows you to swing a bucket of water around in a horizontal circle without spilling any water. • BUT IT IS NOT A FORCE!

  5. angular velocity vs. linear velocity • angular velocity- angular displacement over time, expressed in radians/second • linear velocity- displacement over time (m/s) • v = rω

  6. angular acceleration • Angular acceleration- rate of change of angular velocity over time. (rad/sec2) • ac=v2/r=ω2r

  7. Centripetal force

  8. In case you don’t believe me… • http://www.youtube.com/watch?v=O6yJG_fnJRc • Proof that the a ball will fly off tangent to the circle’s path when the string is cut. • (because it’s too dangerous to throw things round the classroom)

  9. example 1: • A 500.0 g mass is swinging around on a 2.5 m string with one end at a fixed point in the horizontal plane, is travelling along a circular path at a speed of 4.0 m/s.

  10. Q: of the forces acting on the ball, which force is the centripetal force?? • A) gravity • B) normal force • C) tension • D) friction

  11. Q: (neglecting friction) What is the centripetal force acting on the ball? • A) 5.0 N • B)5000 N • C) 3200 N • D) 3.2 N

  12. answer: • D) 3.2 N F=(.5 kg)(4 m/s)2/(2.5 m)=.0 N

  13. Planetary motion • The centripetal force acting on planets to keep them in orbit is gravity.

  14. Q: What physical characteristics of the moon and Earth affect the force of gravity? • i. mass of the moon ii. mass of the Earth iii. distance between bodies iv. Orbital speed of the moon • A) i. ii. & iii. • B) i. iii. & iv. • C) i. ii. & iv. • D) ii. Iii. & iv.

  15. The force of gravity is proportional to the 2 masses and the inverse square of the distance between them. • G is the Gravitational constant: • G= 6.673 x 10-11 m3/(kg sec2)

  16. example 2: • A satellite of mass m1 =8.0 x 1020 kg is orbiting around a planet of mass m2=4.5 x 1023 kg. The difference between their centers of mass is 2.5 x 104 km.

  17. Q: How fast is the satellite travelling? • A) 46.21m/s • B) 3.466 x 104m/s • C) 1.096 x 103m/s • D) 1.461 x 103m/s

  18. Answer: C) v=1.096 x 103m/s

  19. Q: What is the angular velocity of the satellite? • A) 2.74 x 107 rad/sec • B) 2.28 x 104rad/sec • C) .044 rad/sec • D) 4.4 x 10-5rad/sec

  20. Q: What is the angular acceleration of the satellite? • A) 7.7 x 10-17 rad/sec2 • B) .048 rad/sec2 • C) 3.00 x 1013 rad/sec2 • D) 3.3 x 10-13 rad/sec2

  21. Q: How long does it the take satellite to complete one orbit? • A) 39.81 hours • B) 39.81 minutes • C) 2.39 minutes • D) 20.7 days