Roller Coasters - General Physcis - Lecture Slides, Slides of Physics

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Roller Coasters

Uniform or Nonuniform 

Centripetal acceleration is constant for uniformcircular motion.

It changes for

nonuniform

circular motion.

-^

The magnitude increases or decreases.

-^

There is a tangential acceleration.

-^

Net vector is not antiparallel to radius.

2

2

 r

v r a^





Rotational Motion 

Kinematic equations withconstant linear accelerationwere defined.^ •

vav

v^0

v

•^

v^

=^

v^0

at

•^

x^

=^

x^0

v

t 0

at

2

•^

(^2) v

v

(^20)

a (

x^

-^ x



Kinematic equations withconstant angularacceleration are similar.^ •

av^

•^

t

•^

^

=^

^0

t 0

 t

2

•^

(^20)

^

-^

^0

Loop-the-Loop 

A loop-the-loop is a popularrollercoaster feature.



There are only two forcesacting on the moving car.•

Gravity

-^

Normal force



There is a centripetalacceleration due to the loop.

Fg FN

Force at the Top 

The forces of gravity and thenormal force are bothdirected down.



Together these must matchthe centripetal force.



The minimum occurs withalmost no normal force.

Fg

FN

gr

v

gr

m

r

F

v

mg

F

r

mv

F

F

F

N

g N

N

c

min

Speed and Acceleration 

Where is the acceleration greatest on therollercoaster?

Use

a

v

2

/^

r.

-^

High velocity causes large acceleration

-^

Small radius causes large acceleration

Too much acceleration on a ride is fatal!

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Try your own coaster