MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.01
W15D2-2 Table Problem Bicycle Wheel Solution
The center of mass of a bicycle wheel is initially moving with speed v0 to the right and
spinning with angular velocity ω0 . The wheel starts to skid forward on a level surface
until it begins to roll without slipping on a level surface. The moment of inertia of the
wheel about the center of mass is I cm = m R 2 where R is the radius of the wheel and m
is the mass of the wheel. The coefficient of kinetic friction is µ k .
a) Draw a free body diagram of all the forces acting on the bicycle wheel while it is
skidding forward.
b) What is the (i) final angular speed ω f , and (ii) final speed v f , of the wheel when
it begins to roll without slipping?
c) How much time, t f , does it take before the wheel starts to roll without slipping?
We know that because of the rolling without slipping condition that
v f = Rω f =
1
v + Rω 0
2 0
(
)
(1)
c) Newton’s Second Law is
− f k = max .
Integrating this equation yields
v f − v0 = − µ k gt f
(2)
where we used the fact that f k = µ k mg .
tf =
v0 − Rω 0
2µk g
(3)
Substitute Eq. (1) into Eq. (2) and solve for the time it takes to just start to roll without
slipping,
v − Rω 0
.
(4)
tf = 0
2µk g