CHAPTER 5Dynamics of Uniform Circular

MotionUniform Circular Motion

Centripetal Acceleration

Centripetal Force

Satellites in Circular Orbits

Vertical Circular Motion

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.

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

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

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

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