CHAPTER 6 CIRCULAR MOTION
CENTRIPETAL FORCE
The force F necessary to keep a body in uniform circular motion is defined as the
centripetal force. The magnitude of the force is F = m v2/r and it is directed to the center
of rotation. If F were not present object m would move along it’s velocity vector v.
F can be produced by gravitational attraction,
a string, or a roadbed pushing on a tire.
EXIT RAMP (see examples 6-4 and 6-5)
A curved exit ramp is normally inclined to facilitate a higher speed of exit with no
slippage. Consider a car of mass m moving with velocity v along a curved path of radius
R. There is static friction µk between the tire and road. This frictional force f = µk N must
oppose the outward m v2/r force. Then the maximum velocity before slippage is
mv2/r = f = µk N = µk mg
vmax = ( r g µk) 1/2
If the exit ramp is inclined the forces
opposing slippage can be increased.
mv2/r = N sinθ + f cosθ
mg = N cosθ
We can determine the banking angle under extreme conditions f = 0 (ice!!), thus not
relying on frictional forces.
m v2/r = N sinθ
m g = N cosθ
tanθ = v2 /r g
or
vmax = ( r g tan θ ) 1/2
v
F
r
m
r
v
m
ˆF=mv2/r
f
mv2/r
mg
f
N
θ
N cosθ
N sinθ
f cosθ
