Circular MotionUniform and Non-Uniform

ReviewEquations for Motion Along One

Dimension

dtdx

txv

txv

t

ave

0lim

dtdv

tva

tva

t

ave

0lim

ReviewMotion Equations for Constant

Acceleration

•1.

•2.

•3.

•4.

atvv 0

221

00 attvxx

20vvvave

xavv 220

2

ReviewAcceleration in Uniform Circular

Motion

Velocity is always tangent to the pathAcceleration is always perpendicular

to velocityAcceleration is center seeking

(Centripetal)

Rva2

Review3 Laws of MotionIf in Equilibrium

If not in equilibriumChange in Motion is Due to Force

Force causes a change in acceleration!

0F

maF

Acceleration on a Curve

0t

0v

2t

2v

0a

rva2

2a

Acceleration on a Curve

0t

0v

2t

2v

0a

Car is always accelerating

There must be a force acting on the car!

rva2

Force on a Curve

Centripetal Force

0t

0v

2t

2v

0a

rva

amF2

rvmF2

0F

Note: On Centrifugal ForceThere is no such thing as

centrifugal forceIt is merely the action reaction

pair of centripetal force.

Centrifugal Force

Centrifugal force you feel in a turning car is just a result of your inertia trying to maintain a straight line of motion.

Example: Car on a curveA 1,500 kg car is rounding a

curve with radius 35.0 m. If the coefficient of friction is 0.500 find the maximum speed the car can have without slipping.

Example: Car on a curveMax velocity is related to max

acceleration is related to Centripetal force

No slipping means Centripetal Force= Force of

frictionrvmF2

Nf

Example: Car on a curve

smv

v

grvmmgrv

mgrvm

Nrvm

1.13)80.9)(500.0)(0.35(

2

2

2

Example: Car on a banked curveA civil engineer wishes to design

a curved ramp in such a way that a car will not have to rely on friction to round the curve without skidding (in case of rain or ice). This is done by banking the curve (tilted towards one side). If the speed of the ramp is supposed to be 13.4 m/s, and the radius is 50.0m at what angle should the curve be banked?

Example: Car on a banked curve

Example: Car on a banked curve

rvmNF2

sin

cos

cosmgN

mgN

Example: Car on a banked curve

1.20)50)(8.9(

4.13tantan

tan

tan

tan

21

21

2

2

2

grv

grvrvg

rvmmg

Giancoli 5-22A 1200 kg car rounds a curve of

radius 67m banked at 12o. If the car is travelling at 95 kph will a friction force be required? If so, how much and in what direction?

Vertical Uniform Circular MotionA passenger on a Ferris wheel

weighs 750N. The wheel has a radius of 100 m and moves at constant speed of 10.5m/s. Find the apparent weight of the passenger at the top and at the bottom of the wheel.

Vertical Uniform Circular Motion

At top At BottommaF

)(2

2

2

rvgmN

rvmmgN

rvmwNF

)(2

2

2

rvgmN

rvmmgN

rvmwNF

Non- Uniform Circular MotionRadial acceleration – causes

change in directionTangential acceleration – causes

change in speed

Artificial Gravity