Chapter 5

1. Chapter 5 Dynamics of Uniform Circular Motion Uniform Circular Motion Centripetal Acceleration Centripetal Force Satellites in Circular Orbits Vertical Circular Motion

2. Uniform Circular Motion • Uniform circular motion is the motion of an object traveling at a constant speed on a circular path • Period (T) is the time required to make one complete revolution • V = 2 p r / T • Magnitude of the velocity vector is constant, however, the vector changes direction and is therefore accelerating. This is known as centripetal acceleration.

3. Centripetal Acceleration • Magnitude: • The centripetal acceleration can be calculated by the following Ac = v2/r • Direction: • The centripetal acceleration vector always points toward the center of the circle and continually changes direction as the object moves. **The centripetal acceleration is smaller when the radius is larger • Pg 155 #1, 3, pg 156 #1, 5, 9

4. Centripetal Force • Newton’s second law indicates that when an object accelerates there must be a net force to create the acceleration. The centripetal force points in the same direction as the acceleration (toward the center) and can be calculated as follows: Fc = mv2/r • Name given to the net force required to keep an object of mass m, moving at speed v, on circular path of radius r. • Pg 155 #7, pg 156 #13, 15, 21

5. Satellites in Circular Orbits • There is only one speed that a satellite can have if the satellite is to remain in orbit with a fixed radius. • For a given orbit, a satellite with a large mass has exactly the same orbital speed as a satellite with a small mass. • See pg 144-145 ex 9 • Pg 155 #11, pg 158 #31, 33

6. Vertical Circular Motion • There are 4 points in a vertical circle where the centripetal force can be identified. The centripetal force is the net sum of all of the force components oriented/pointing toward the center of the circle. EX pg 151 • Pg 155 #15, pg 158 #41, 43, 45, pg 159 # 59