A disk has mass 5 kg and outer radius 30 cm
with a radial mass distribution (which may
not be uniform) so that its moment of inertia
is
8/9mR^2 . The disk is rotating at angular
speed 3 rad/s around its axis when it touches
the surface, as shown. The disk is carefully
lowered onto a horizontal surface and released
at time t0 with zero initial linear velocity
along the surface. Assume that when the disk
lands on the surface it does not bounce. The
coefficient of friction between the disk and the
surface is 0.06 .
The kinetic friction force between the sur-
face and the disk slows down the rotation of
the disk and at the same time gives it a hor-
izontal acceleration. Eventually, the diskâs
linear motion catches up with its rotation,
and the disk begins to roll (at time trolling)
without slipping on the surface.
5 kg
3 rad/s
µ = 0.06
How long after the kick does it take for the
ball to roll without slipping? The acceleration
of gravity is 9.8 m/s2 .
Answer in units of s.
A disk has mass 5 kg and outer radius 30 cm
with a radial mass distribution (which may
not be uniform) so that its moment of inertia
is
8/9mR^2 . The disk is rotating at angular
speed 3 rad/s around its axis when it touches
the surface, as shown. The disk is carefully
lowered onto a horizontal surface and released
at time t0 with zero initial linear velocity
along the surface. Assume that when the disk
lands on the surface it does not bounce. The
coefficient of friction between the disk and the
surface is 0.06 .
The kinetic friction force between the sur-
face and the disk slows down the rotation of
the disk and at the same time gives it a hor-
izontal acceleration. Eventually, the diskâs
linear motion catches up with its rotation,
and the disk begins to roll (at time trolling)
without slipping on the surface.
5 kg
3 rad/s
µ = 0.06
How long after the kick does it take for the
ball to roll without slipping? The acceleration
of gravity is 9.8 m/s2 .
Answer in units of s.
