1. Centripetal Force Applications
Circus cycle show

2. The Maximum Speed to Travel in a Horizontal Circular Path
f=Fc
f=uN
f=μW
μmg= mv2/r
μg=v2/r f
Maximum speed to
round a horizontal
circular path. f f W r f N
Minimum μ to
round circular path.
W=N
on a flat, level surface.

3. An object traveling in a vertical circle:

4. The Force on a Mass Traveling in a Vertical Circular Path
Fnet=Fc
Forces towards the center of the
circular path are positive and forces
away from the center from the circular
path are negative.
At the path bottom:
F-W=mac
F=W+mac
At path top:
F+W=mac
F=-W+mac
The forces at the
top of the circular
vertical path.
There is a smaller force applied at the
top of the path than the bottom because
gravity aids in the centripetal force on
the top of the path. The force has to
overcome gravity on the bottom of the path. F W
Minimum speed needed to
round a vertical circle:
F=0 if there is not enough speed
to round the vertical circle
0=W-mac mac=mg ac=g*v2/r=g F
*The centripetal acceleration must
at least be equal to g (9.8 m/s2).
The forces on the
bottom of a vertical
circular path. or W
Minimum speed needed to
round a vertical circular path

5. Vertical Suspension while Traveling a Horizontal Circle
forces
ΣFx = Fc
N = Fc f
ΣFy = 0
f-w=0  W=f
mg=μN  mg=μ(Fc)
mg=μ(mv2/r)g=μv2/r N Fc
Horizontal
forces
Minimum speed need for an object to
remain vertically suspended while
traveling around in a horizontal
circlur path. W r

6. An object spinning horizontally at the end of a string that makes an angle:
ΣFx=Fc
Tx=Fc
Tx=mac
Tcosθ=mac T
ΣFy=0
Ty-W=0Ty=W
Tsinθ=W
Tsinθ=mg Ty θ Tx r
Since T is a variable in both equations,
then the two equations can be combined
into one, giving  W

7. Equation Summary F = W+mac F = -W+mac
The maximum speed an object can travel in a circular horizontal path without sliding. .
The minimum coefficient of friction needed for an object to travel in a horizontal circular path without sliding.
The force exerted on an object traveling in a vertical circular path at the bottom
F = W+mac
F = -W+mac
The force exerted on an object traveling in a vertical circular path at the top.
The minimum speed needed to travel in a vertical circular path.
The minimum speed needed to remain vertically suspended while traveling in a horizontal circular path.
A relationship between the angle, acceleration due to gravity, and centripetal acceleration for a mass at the end of a string, rope, or chain that is whirled in a horizontal circular path.