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Uniform Circular Motion and Centripetal Acceleration

Uniform Circular Motion and Centripetal Acceleration. 5.1 and 5.2. 5.1 Uniform Circular Motion. Object is traveling at a constant (uniform) speed on a circular path Period (T) – Time it takes to make one trip around the circle Circumference – distance around the circle C = 2 r.

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Uniform Circular Motion and Centripetal Acceleration

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  1. Uniform Circular Motion and Centripetal Acceleration 5.1 and 5.2

  2. 5.1 Uniform Circular Motion • Object is traveling at a constant (uniform) speed on a circular path • Period(T) – Time it takes to make one trip around the circle • Circumference – distance around the circle • C = 2r

  3. Uniform Circular Motion • Speed (v) – distance / time • Find v • v = 3.77 m/s 1.2 m T=2s

  4. Uniform Circular Motion • Speed is constant • Velocity is not constant • Velocity is always changing • This acceleration is “centripetal” acceleration

  5. 5.2 Centripetal Acceleration • Object moves in circular path • At time t0 it is at point O with a velocity tangent to the circle • At time t, it is at point P with a velocity tangent to the circle • The radius has moved through angle 

  6. Centripetal Acceleration • Draw the two velocity vectors so that they have the same tails. • The vector connecting the heads is v • Draw the triangle made by the change in position and you get the triangle in (b)

  7. Centripetal Acceleration • Since the triangles have the same angle are isosceles, they are similar

  8. Centripetal Acceleration

  9. Centripetal Acceleration Know this

  10. Centripetal Acceleration • At any given moment • v is pointing tangent to the circle • ac is pointing towards the center of the circle • If the object suddenly broke from circular motion would travel in line tangent to circle

  11. Example 1 • Two identical cars are going around two corners at 30 m/s. Each car can handle up to 1 g. The radius of the first curve is 50m and the radius of the second is 100 m. Do either of the cars make the curve? (hint find the ac) • Yes, 100m 50 m 100 m

  12. Problems • Try this! • Page 142 CQ 1-5, P1, 2, 5 – 8, 10 • Total of 12 Problems

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