Transcript Rotational Motion

A microwave oven has a rotating
plate 30 cm in diameter. From rest
the plate accelerates at a uniform
2
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
rim?
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
F
1
θ1
r
θ2
A
r
2
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
balanced?
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
scale
scale
¼L
L
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
1m
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?
A
B
C
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
angular
12 cm
acceleration
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
2
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
turntable?