# Circular and Satellite Motion - Mission CG4 Detailed Help

 A bucket of water is held by a rope and twirled in a vertical circle. The bucket is whirled more rapidly such that the speeds at both the top and the bottom of the circle are increased. As this increase in speed occurs, the _____. List all that apply ... .
 Centripetal Force Requirement: Circular motion requires an inward force. To travel along the curved path of a circle, there must be a force directed centripetally. Any object or thing could supply the force as long as it is directed toward the center of the circular path.
 The acceleration (a) of an object moving in a circle is dependent upon the speed (v) of the object and the radius (R) of the circle. The relationship is expressed by the following equation: a = v2/R
 Circular motion requires an inward force to cause the inward acceleration. The acceleration that is needed is dependent in part upon the speed of the bucket. Consistent with the equation in the Formula Frenzy section, an increase in speed will cause the acceleration to increase. As would be reasoned from Newton's second law (Fnet = m•a), an increase in acceleration would require an increased net force. The net force is the vector sum of the two individual forces - gravity and tension. The force of gravity is dependent upon the object's mass and unaffected by a change in speed. Thus, the increased net force must result from an increase in the magnitude of the tension force.