UNIFORM CIRCULAR MOTION AND GRAVITATION Uniform Circular Motion Centripetal Force Gravitation Kepler’s Laws Gravitational Potential Energy

Any object traveling in a circular path, or section of a circular path, is in circular motion. If the object’s speed is constant during this motion, the motion is called uniform circular motion. EXAMPLES: A ball being swung in a horizontal, circular path at the end of a string A car going around a turn A roller coaster car going over a hill or loop, or around a turn An airplane in a turn or loop A satellite in orbit

If T is measured in years and r is measured in astronomical units, then This is useful only for planets.

GRAVITATIONAL POTENTIAL ENERGY: Previously, we studied gravitational potential energy for objects near the earth’s surface and not experiencing large changes in elevation. In such cases, the free-fall acceleration, g, is very nearly constant and was treated as so. We used PE = mgh for an object’s potential energy where h was measured from an arbitrary reference. Now we are going to consider objects moving over great distances and not close to the surface; distances over which the value of g changes significantly. In such cases, an object’s potential energy is set to zero when it is infinitely far from earth. As the object approaches earth, its potential energy is negative and decreases the closer it gets. The equation used for gravitational potential energy for an object of mass m object in this case is: r is measured form the center of the earth.

EXAMPLE:Calculate the escape velocity from the earth for an object at rest on its surface. The escape velocity is the minimum speed needed by an object to escape the gravitational influence of earth without ever falling back or needing additional thrust.

ANSWER:Calculate the escape velocity from the earth for an object at rest on its surface. The escape velocity is the minimum speed needed by an object to escape the gravitational influence of earth without ever falling back or needing additional thrust.