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Circular Motion

Circular Motion. AP Physics B Chapter 5 Notes. Uniform Circular Motion. Consider an object moving in a circle around a specific origin. The DISTANCE the object covers in ONE REVOLUTION is called the CIRCUMFERENCE . The TIME that it takes to cover this distance is called the PERIOD .

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Circular Motion

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  1. Circular Motion AP Physics B Chapter 5 Notes

  2. Uniform Circular Motion Consider an object moving in a circle around a specific origin. The DISTANCE the object covers in ONE REVOLUTION is called the CIRCUMFERENCE. The TIME that it takes to cover this distance is called the PERIOD. Speed is the MAGNITUDE of the velocity. And while the speed may be constant, the VELOCITY is NOT. Since velocity is a vector with BOTH magnitude AND direction, we see that the direction of velocity is ALWAYS changing. We call this velocity, TANGENTIAL velocity as its direction is draw TANGENT to the circle.

  3. Centripetal Acceleration • If velocity is changing, the object must be accelerated • This is called centripetal acceleration (“center seeking”)

  4. Centripetal Acceleration Formula • As an object moves from A to B, it sweeps out an arc of Δl, and Δθ degrees • The difference in the velocities over Δθ is Δv (b)

  5. Centripetal Acceleration Formula • As we look at a shorter time period, Δland Δθ approach zero and Δv points toward the center of the circle—the same direction as a • a = and as Δt 0, and so or

  6. Centripetal Force • A net force must be acting on the object moving in a circle • So:

  7. Centripetal Force • The net force acts inward—think of tension on a string • Other useful formulae:

  8. More Complicated Example • If a pig could fly, and you knew the angle it swept out and how long a string was that held it in a circle, could you find its velocity?

  9. Applications to Turning • When you make a turn in a car, you feel like you are being pushed out the door • You are feeling inertia, not a force pushing you out • A force has to push you in

  10. Applications to Turning--Example • Example 5-6 pg. 113: A 1000 kg car rounds a curve on a flat road of radius 50 m at a speed of 50 km/h (14 m/s). Will the car follow the curve, or will it skid? Assume a) pavement is dry μ = 0.60 b) pavement is wet μ = 0.25. Bad commute day

  11. Centripetal Acceleration—Vertical Circle • When an object moves in a vertical circle you have to consider gravity…

  12. Applications to Turning--Example Banking a turn allows a component of the normal force to contribute to centripetal force in addition to friction

  13. Circular Motion Summary • For an object moving in a circle: • Velocity is tangent to the circle • Acceleration is toward the center of the circle • If acceleration ceases, inertia causes the object to move in a straight line (tangent) • Velocity and acceleration are found by:

  14. Newton’s Universal Law of Gravitation • Newton wondered what was the source of the force causing g • Concluded it was Earth itself • Extrapolated falling apple to moon

  15. Newton’s Universal Law of Gravitation • Newton knew the moon’s orbital radius and its velocity, so he reasoned • He also realized that the magnitude of the force was proportional to both masses • Thus he proposed: G was later determined to be 6.67 x 10-11 Nm2/kg2

  16. Implications of ULG • P 28 pg 131: Calculate the force of gravity on a spacecraft 12,800km (2 Earth radii) above the Earth’s surface if its mass is 1350kg. • Gravity near the Earth’s surface is not exactly constant:

  17. Satellites • What keeps a satellite in orbit? • Its speed—it falls to Earth just enough to counteract its tangential speed • Notion of escape velocity

  18. Example 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

  19. Weightlessness • Consider and elevator ride—when do you feel heavy or light? • What if a = g? Apparent weightlessness

  20. Kepler’s Laws • The path of a planet about the Sun is an ellipse • Each planet moves so that it sweeps out equal areas in equal periods of time

  21. Kepler’s Laws • The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their distance from the sun. Derivation:

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