Section 5-2 Circular Motion; Gravitation

Objectives: The student will be able to: identify the type of force supplying the centripetal force that acts on any object in uniform circular motion. determine the directions of the velocity, acceleration, and net force vectors for an object in uniform circular motion. identify centrifugal force as a fictitious force and explain how it results from an accelerated frame of reference. use Newton's laws of motion and the concept of centripetal acceleration to solve word problems.

February 18, 2016 Uniform Circular Motion: Observations  Object moving along a curved path with constant speed Magnitude of velocity: same Direction of velocity: changing Velocity : changing Acceleration is NOT zero! Net force acting on an object is NOT zero “Centripetal force”

5-2 Dynamics of Uniform Circular Motion For an object to be in uniform circular motion, there must be a net force acting on it. We already know the acceleration, so can immediately write the force: (5-1)

Uniform Circular Motion : Newton’s 2nd Law: The net force on a body is equal to the product of the mass of the body and the acceleration of the body. *The centripetal acceleration is caused by a centripetal force that is directed towards the center of the circle.

5-2 Dynamics of Uniform Circular Motion We can see that the force must be inward by thinking about a ball on a string: Demo – penny and hanger

5-2 Dynamics of Uniform Circular Motion There is no centrifugal force pointing outward; what happens is that the natural tendency of the object to move in a straight line must be overcome. If the centripetal force vanishes, the object flies off tangent to the circle.

“Centrifugal Force” “centrifugal force” is a fictitious force - it is not an interaction between 2 objects, and therefore not a real force.“centrifugal force” is a fictitious force - it is not an interaction between 2 objects, and therefore not a real force. Nothing pulls an object away from the center of the circle.Nothing pulls an object away from the center of the circle.

“Centrifugal Force” What is erroneously attributed to “centrifugal force” is actually the action of the object’s inertia - whatever velocity it has (speed + direction) it wants to keep.What is erroneously attributed to “centrifugal force” is actually the action of the object’s inertia - whatever velocity it has (speed + direction) it wants to keep.

February 18, 2016 Centripetal Force Acceleration: –Magnitude: –Direction: toward the center of the circle of motion Force: –Start from Newton’s 2 nd Law –Magnitude: –Direction: toward the center of the circle of motion

February 18, 2016 What provides Centripetal Force ? Centripetal force is not a new kind of force Centripetal force refers to any force that keeps an object following a circular path Centripetal force is a combination of –Gravitational force mg : downward to the ground –Normal force N : perpendicular to the surface –Tension force T : along the cord and away from object –Static friction force: f s max = µ s N

February 18, 2016 a What provides Centripetal Force ? mg N v

Example Problem A 2.0-kg mass is attached to the end of a 3.0 m-long rope and spun in a vertical circle at a speed of 6.6 m/s. Determine the maximum and minimum tensions in the rope.

February 18, 2016 Problem Solving Strategy Draw a free body diagram, showing and labeling all the forces acting on the object(s) Choose a coordinate system that has one axis perpendicular to the circular path and the other axis tangent to the circular path Find the net force toward the center of the circular path (this is the force that causes the centripetal acceleration, F C ) Use Newton’s second law –The directions will be radial, normal, and tangential –The acceleration in the radial direction will be the centripetal acceleration Solve for the unknown(s)

Homework for Section 5-2 Problems 7, 8, 9, 13, 16, 18

Kahoot Section 5-2 Giancoli Dynamics of Uniform Acceleration