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Circular Motion and Gravitation

Circular Motion and Gravitation. An object moving in a circle at constant speed experiences uniform circular motion Acceleration points towards the center Therefore this acceleration is called centripetal acceleration or radial acceleration Centripetal acceleration, a R = v 2 / r

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Circular Motion and Gravitation

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  1. Circular Motion and Gravitation • An object moving in a circle at constant speed experiences uniform circular motion • Acceleration points towards the center • Therefore this acceleration is called centripetal acceleration or radial acceleration • Centripetal acceleration, aR = v2 / r • Circular motion is often described in terms of frequency (f in rps) and period (T) = 1/f Chapter 5: Circular Motion - Christopher Chui

  2. Dynamics of Circular Motion • Force is needed to provide centripetal acceleration • The net force must be directed toward the center of the circle • Centripetal force is not a new kind of force • FR = maR = mv2 / r must be applied by other objects • There is no centrifugal (outward) force • For a revolving ball in a vertical circle, gravity and cord tension together provide centripetal acceleration • String tension and gravity acting in opposite directions provide centripetal acceleration Chapter 5: Circular Motion - Christopher Chui

  3. Newton’s Law of Universal Gravitation • Every particle in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This force acts along the line joining the two forces: F = G m1m2 / r2 • G = 6.67 x 10-11 N-m2/kg2 • Gravity near the earth’s surface: mg = GmmE/rE2 Chapter 5: Circular Motion - Christopher Chui

  4. Kepler’s Laws • 1st Law: The path of each planet about the sun is an ellipse with the sun at one focus • 2nd Law: Each planet moves so that an imaginary line drawn from the sun to the planet sweeps out equal areas in equal periods of time • 3rd Law: The ratio of the squares of the periods of any two planets revolving about the sun is equal to the ratio of the cubes of their mean distances from the sun Chapter 5: Circular Motion - Christopher Chui

  5. Types of Forces in Nature • The gravitational force • The electromagnetic force • The strong nuclear force • The weak nuclear force • Electromagnetic and weak forces are manifestations of a single electroweak force • Everyday forces are gravity and electromagnetic • Attempts to unify the forces are hot research topics today, such as the grand unified theories (GUT) Chapter 5: Circular Motion - Christopher Chui

  6. Problem Solving Technique • Draw a free-body diagram showing all the forces acting on each object under consideration • Determine which of these forces act to provide the centripetal acceleration (all the forces that act radially, toward or away from the center of the circular path) • Choose a coordinate system, and +ve and –ve directions, and apply Newton’s 2nd law • For the gravitational force, use Newton’s law of universal gravitation; be sure to put the correct value for r. For large objects, r is measured from the center Chapter 5: Circular Motion - Christopher Chui

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