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Uniform Circular Motion

Uniform Circular Motion. Wednesday, July 30, 2014. Uniform Circular Motion. An object that moves at uniform speed in a circle of constant radius is said to be in uniform circular motion . Uniform circular motion is accelerated motion

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Uniform Circular Motion

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  1. Uniform Circular Motion Wednesday, July 30, 2014

  2. Uniform Circular Motion • An object that moves at uniform speed in a circle of constant radius is said to be in uniform circular motion. • Uniform circular motion is accelerated motion • Although the speed is constant, the velocity is not constant since an object in uniform circular motion is continually changing direction.

  3. Centrifugal Force • Question: What is centrifugal force? • Answer: Centrifugal force is the force that flings an object in circular motion outward. Right? • Wrong. There is no outward directed force in circular motion. Inertia makes you feel like you are being propelled outward.

  4. When a car turns • You feel as if you are flung to the outside. You call this apparent, but nonexistent, force “centrifugal force”. • You are NOT flung to the outside. Your inertia resists the inward acceleration andyour body simply wants to keep moving in a straight line

  5. Centripetal Acceleration • Centripetal (center-seeking) acceleration points toward the center of the circle and keeps an object moving in circular motion. • This type of acceleration is at right angles to the velocity. • This type of acceleration doesn’t speed up an object, or slow it down, it just turns the object.

  6. ac v Centripetal Acceleration ac = v2/r • ac: centripetal acceleration in m/s2 • v: tangential speed in m/s • r: radius in meters Centripetal acceleration always points toward center of circle!

  7. Centripetal Force • A force responsible for centripetal acceleration is referred to as a centripetal force. • Centripetal force is simply mass times centripetal acceleration. • Fc = mac • Fc = mv2 / r • Fc: centripetal force in N • v: tangential speed in m/s • r: radius in meters Fc Always toward center of circle!

  8. Any force can be centripetal • The name “centripetal” can be applied to any force in situations when that force is causing an object to move in a circle. • You can identify the real force or combination of forces which are causing the centripetal acceleration. • Any kind of force can act as a centripetal force.

  9. Universal Gravitation July 30, 2014

  10. Law of Universal Gravitation • Newton’s famous apple fell on his head and lead to this law. • It tells us that the force of gravity objects exert on each other depends on their masses and the distance they are separated from each other.

  11. Force of Gravity • Fg = mg, right? • Yes and No. We’ve use this to approximate the force of gravity on an object near the earth’s surface. • This formula won’t work for planets and space travel. It also won’t work for objects that are far from the earth.

  12. Force of Gravity • Fg: Force due to gravity (N) • G: Universal gravitational constant • 6.67 x 10-11 N m2/kg2 • m1 and m2: the two masses (kg) • r: the distance between the centers of the masses (m) • The Universal Law of Gravity ALWAYS works, whereas F = mg only works locally.

  13. Sample Problem • How much force does the earth exert on the moon? • How much force does the moon exert on the earth?

  14. Sample Problem • Which has more gravitational influence on you: Jupiter (1.9x1027 kg, 9x1011 km) or the person sitting right next to you (60 kg, 1 m)

  15. Acceleration due to Gravity • g = GM/r2 • Stems from F = mg and F = Gm1m2/r2 • This formula lets you calculate g anywhere if you know the distance a body is from the center of a planet.

  16. Relationships • Gravitational forces DECREASE as 1/r2. • Gravity is said to decrease as the INVERSE SQUARE LAW. • Calculus is necessary to show that the gravitational acceleration inside a body decreases linearly.

  17. Kepler’s Laws July 30, 2014

  18. Johannes Kepler • Kepler developed some extremely important laws about planetary motion. • Kepler based his laws on massive amounts of data collected by Tycho Brahe. • Kepler’s laws were used by Newton in the development of his own laws.

  19. Kepler’s Laws 1. Planets orbit the sun in elliptical orbits, with the sun at a focus. 2. Planets orbiting the sun carve out equal area triangles in equal times. 3. The planet’s year is related to its distance from the sun in a predictable way.

  20. Kepler’s Laws: 1 & 2 • http://surendranath.tripod.com/Applets.html

  21. Gravity as a Centripetal Force • The orbits we analyze mathematically will be nearly circular. • Fg = Fc • centripetal force is provided by gravity) GMm/r2 = mv2/r • The mass of the orbiting body cancels out in the expression above. One of the r’s cancels as well

  22. Sample Problem • What velocity does a satellite in orbit about the earth at an altitude of 25,000 km have? What is the period of this satellite?

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