Rotational Motion

A microwave oven has a rotating
plate 30 cm in diameter. From rest
the plate accelerates at a uniform
rate of 0.87 rad/s for 0.5 s.
a. How many revolutions does
the plate make before reaching
operational speed?
b. What are the angular and
tangential speeds of the object at the
A small coin is placed on a turntable
that makes 3 revolutions in 3.14 s.
What is the speed of the coin when it
rides 5 cm away from the center? If
the mass of the coin is 2 g, what is the
frictional force acting on it? If the
coin slides off when it is
placed 10 cm away from
the center, what is μs?
A CD accelerates uniformly from
rest to operational speed of 500
RPM (revolutions per minute) in
3.5 s. What is the angular
acceleration of the CD? If the CD
comes to a rest 4.5 s, what is the
angular acceleration? How many
revolutions occur during this time?
The object is pivoted at A and
two forces act on it as shown.
If r1= 1.3 m and r2 = 2.15 m,
F1= 4.2 N and F2 = 4.9 N, θ1=
75° and θ2 = 60°, what is the
net torque?F
Tracy is building a mobile.
Equilibrium: mobile
She hangs a 0.02 kg sailboat
0.1 m from the left end and a
0.015 kg truck 0.2 m from the
right end of a bar 0.5 m long.
Where must the support string
be placed such that it is
A beam of length L, whose mass is
1.8 kg rests w/ its ends on 2 digital
scales. A block w/ M = 2.7 kg rests
on the beam a distance ¼ L from the
beam’s left end. What do the
two scales read?
Equilibrium: board on 2 scales
Bob the window washer is
Equilibrium: window washers
standing on a hanging
scaffold supported by a
vertical rope at each end.
The scaffold weighs 205 N
and is 3 m long. What is the
force each rope exerts on the
scaffold when a 675 N Bob
stands 1 m from the right
A ladder ml = 15 kg rest against
a smooth wall (frictionless).
Paul the painter with mp = 78
kg stands on the ladder.
What frictional
force must act
on the ladder
5.6 m
to keep it
from slipping?
1.6 m
Ex: A toy consisting of two balls,
each 0.45 kg at the ends of a 0.46
m long, thin, lightweight rod is
shown. Find the moment of
inertia of the toy about the center
of the rod.
Each sphere has a mass of 0.1 kg. The
distance between each sphere is 0.2 m.
Find the moment of inertia if the
rotation is about A. About B?
Consider the following solid cylinder
with two forces acting on it. If the
mass of the cylinder is 50 kg,
determine the
100 N
80 N
12 cm
produced by
8 cm
the two forces.
If the radius of a basketball
is 12 cm and the mass is 0.6
kg, determine the angular
acceleration of the ball if it
rolls down an incline of 5
degrees. How far does the
ball roll in 1.4 seconds?
A 2 kg sphere with a radius of 25 cm
rolls (without slipping) down an
inclined plane of height 0.3 m and
length 0.5 m. Determine the linear
speed of the cylinder’s
center of mass
when it reaches
the bottom of
the incline.
A block with a mass of m = 5 kg
is hung from a pulley of radius
15 cm and a mass M = 8 kg and
then released from rest. What is
the speed of the block as it
strikes the floor 2 m below its
initial position? What is the
rotational kinetic energy of the
pulley just before the block
strikes the floor? At what rate
was work done on the pulley?
Ex: A child of mass m = 30 kg stands at
the edge of a small merry-go-round
that’s rotating at a rate of 1 rad/s. The
merry-go-round is a disk of radius R =
2.5 m and a mass of M = 100 kg. If the
child walks in, toward the center of the
disk and stops 0.5 m from the center,
what will happen to the angular
velocity of the merry-go-round (neglect
an effects due to friction)?
A student sits on a rotating stool
holding two 3 kg masses. When his
arms are extended horizontally the
masses are 1 m from the axis of
rotation. He rotates with angular
speed of 0.75 rad/s, and the moment
of inertia of the student-stool is 3
kgm . The student then pulls the
masses to 0.3 m, what is the new
angular speed?
A 55 kg person stands at the edge
of a 6.5 m diameter turntable that
has a moment of inertia of 1700
kgm2. The turntable is stationary
until the person begins running
on the turntable w/ a v = 3.8 m/s.
What is the angular velocity of the