1. Physics of Amusement Park Rides
The Carousel
Ferris Wheel
Loop-the-Loop
The Rotor

2. The Carousel: An Example of Uniform Circular Motion
Turning about axis O
w/ Constant Angular Speed 
Axis O

3. Draw the Forces on the Rider
What is the nature of the net force on
the rider ? Where is this pointing ?
Central force pointing to O
What provides the net force on him ?
The normal support force
of the back of the seat
What kind of net force along the y-axis ?
Is there motion along y ?
y: stationary uniform motion
What is the sensation he feels ?
Pressed against the chair
(or alternatively, chair pressing against his back)
How can this be enhanced ?
Increase  O y
N’ = mg
N = mv2/R x mg

4. The Ferris Wheel “Weightless” Feeling at the top ‘Heavy’ feeling at
the bottom

5. Draw the Forces on the Rider constant  2
What is the nature of the net force on
the rider ? Where is this pointing ?
a central force mg
At 2: mg - N = mv2/R
or N = mg - mv2/R
‘feels lighter’ 1
At 1: N - mg = mv2/R
or N = mg + mv2/R
‘feels heavier’ 3 N
What is the sensation he feels
At locations 2 and 4 ? 4 mg
What happens if the rotational speed is increased beyond (gR)1/2?
He flies off upon reaching position 2

6. The Roller Coaster
SLOW
FAST
Weightless Sensation
Heavy Sensation

7. How is Energy conserved in the roller coaster ride ?
Potential Energy = mgh
Kinetic Energy= 0 A. C
Vo = 0 h R
B. KE = (1/2) mv2
PE = 0
To clear the top of the loop, h  2R.
In fact, ignoring friction, minimum h = 2.5 R

8. Draw the Forces on the Rider constant 
What is the nature of the net force on
the rider ? Where is this pointing ?
A central force towards O 2 v
At 2: N + mg = mv2/R
or N = mv2/R - mg
Radius R N mg 1 O
At 1: N - mg = mv2/R
or N = mg + mv2/R N 3
What is the sensation he feels
at locations 2 and 4 ?
Heavier at 4, lighter at 2 4 mg
What happens if the speed v is decreased below (gR)1/2?
Rider falls out of car at 2, if not wearing harness.

9. The Rotor Radius R A large cylinder spins.
You are thrown and pinned against the wall.
The floor then slides out.
Yet you do not fall.

10. Draw the forces on the rider ‘pinned’ to the rotor’s wall:
Friction
f = N
N= Fc = mv2/R
rotor wall
Floor pulled out mg
The central force Fc is provided by the normal or
support force N from the rotor’s walls.
For a minimum rotor speed, the normal force is large enough
that the friction f is enough to overcome the weight mg, keeping
the man pinned to the wall.
The critical minimum speed is solved from mg = N = mv2/R
or v = (gR/)1/2