Chapter 5 Uniform Circular Motion

Chapter 5 Objectives (*vocab) 1. Centripetal Acceleration centripetal* uniform circular motion* period* formula for a c 2. Centripetal Force centrifugal* 3. Banked Curves 4. Satellites & Apparent Weight artificial gravity*

5.1 Uniform Circular Motion (U.C.M.) Constant circular speed Velocity is always changing and tangent to the path. Acceleration is towards the center of the circle. Conditions for U.C.M.

5.1 Uniform Circular Motion (U.C.M.)

Period (T) – time required to travel one revolution 5.1 Uniform Circular Motion (U.C.M.)

An object in U.C.M. is always accelerating b/c the direction is always changing. a c = centripetal accleration 5.2 Centripetal Acceleration (a c ) Centripetal means ‘center-seeking’

Centripetal Force – any force directed toward the center of a circle. ‘center-seeking’ The centripetal force keeps an object moving in a circular path; without this force, the object would fly off tangent to the path. 5.2 Centripetal Force (F c )

Examples of Centripetal Force Friction Tension Gravity REMEMBER: Centripetal force is NOT a new type of force; it is just any force that keeps an object in circular motion.

Centrifugal Force – fictitious force arising from circular motion and inertia. “center-fleeing’

Motion in a Vertical Circle

Example : A ball is spinning in a vertical circle at the end of a string that is 2.0m long. If the ball has a mass of 3.5kg and moves at a constant speed of 8.0m/s… a)Calculate the centripetal force that keeps the ball from flying away. Does this force change as the ball moves around the circle? b)What two forces contribute to the centripetal force at the top of the circle? Calculate their values. c)What two forces contribute to the centripetal force at the bottom of the circle? Calculate their values. 112N, this force remains constant Weight = 34 N, Tension = 78N Weight = 34 N, Tension = 146 N

Water will ‘flee’ out of the bucket if the bottom of the bucket did not provide a centripetal force.

In this case, water will ‘flee’ out of the hole in the bucket because of an absence of a centripetal force, NOT because of a centrifugal force.

Objects inside the car will ‘flee’ from the circular path because of INERTIA and the absence of a centripetal (center-seeking) force NOT because of a outward force.

Centrifugal Force is NOT a real force! It is due to inertia and circular motion.

Concept Check: True or False: 1. An object moving in circular motion at a constant speed is accelerating. 2. If an object is moving in circular motion, there must be a centripetal force acting on the object at all times. 3. As a car rounds a corner at a constant speed, the car is accelerating. 4. Without a centripetal force, an object can not move in circular motion. 5. As an object moves in circular motion, a centrifugal force will always push objects away from the center. True False

A ball is swung in circular motion as shown. 6. Draw the direction of the velocity vector. 7. Draw the direction of the acceleration vector. v a

Homework #1: Ch. 5 #1, 2, 3, 6, 8 p. 148

Homework #2: Ch. 5 #13, 15, 18 p. 148

When a car rounds a banked curve, the normal force of the road supplies a centripetal force 5.4 Banked Curves

F c = F N sinθ 5.4 Banked Curves

PRACTICE: Ch. 5 #12-22 (evens only) p. 148

v 1 – v 2 is NOT zero, even though v 1 = v 2

These triangles are similar

a c = centripetal accleration