Circular Motion and the Law of Universal Gravitation

An object moving at constant speed in a circle is in uniform circular motion.

In such motion, there is a distance, r, that moving objects are from the center of the circle. r=radius.

The distance an object travels is the circumference it moves through. This is given by 2  r. x = 2  r

The velocity can be found with v =x/t. Or, in our case, v=2  r/T, where T = the time of one revolution.

Centripetal acceleration is found as a c = v 2 /r. It is always directed toward the center of the circle.

5.2 Centripetal Acceleration Conceptual Example 1: Which Way Will the Object Go? An object is in uniform circular motion. At point O it is released from its circular path. Does the object move along the straight path between O and A or along the circular arc between points O and P ?

The centripetal force an object experiences is given by F =ma, or, F c = mv 2 /r

5.4 Banked Curves On an unbanked curve, the static frictional force provides the centripetal force.

5.4 Banked Curves On a frictionless banked curve, the centripetal force is the horizontal component of the normal force. The vertical component of the normal force balances the car’s weight.

Newton’s Law of Universal Gravitation Every particle in the universe exerts an attractive force on every other particle. A particle is a piece of matter, small enough in size to be regarded as a mathematical point. The force that each exerts on the other is directed along the line joining the particles.

For two particles that have masses m 1 and m 2 and are separated by a distance r, the force has a magnitude given by

4.7 The Gravitational Force

Relation Between Mass and Weight

5.5 Satellites in Circular Orbits There is only one speed that a satellite can have if the satellite is to remain in an orbit with a fixed radius.

5.5 Satellites in Circular Orbits Notice that gravity is providing the centripetal force.

5.5 Satellites in Circular Orbits Example: Orbital Speed of the Hubble Space Telescope Determine the speed of the Hubble Space Telescope Orbiting at a height of 598 km above the earth’s surface.