Chapter 5Uniform Circular Motion

Chapter 5 Objectives (*vocab)

1. Centripetal Accelerationcentripetal*uniform circular motion*period*formula for ac

2. Centripetal Forcecentrifugal*

3. Banked Curves

4. Satellites & Apparent Weightartificial gravity*

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

Circumference (C)

Diameter (d) 3 .1 4 1 5 9 ...

C d

2C r

C

d

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

Period (T) – time required to travel one revolution

distancev =

time

2 r

T

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

An object in U.C.M. is always accelerating b/c the direction is always changing.

ac = centripetal accleration

5.2 Centripetal Acceleration (ac)

Centripetal means ‘center-seeking’

2

c

va

r

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 (Fc)

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

True

True

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

Fc = FNsinθ

5.4 Banked Curves

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

p. 148

v1 – v2 is NOT zero, even though v1 = v2

These triangles are similar

v r

v r

v v t

v r

2v v

t r

2

cva r

as 0,t r v t

2

cva r

ac = centripetal accleration