The diameter of the dwarf
planet, Pluto, is just 2.3 x 106
m. If a space probe were to
orbit Pluto near the planet’s
surface, what would the arc
length of the probe’s
displacement be after
it had completed
eight orbits?
Of the solar system’s planets, the
one whose orbit around the sun is
most circular is Venus. The mean
radius of Venus’s orbit is 1.08 x 1011
m. What arc length
does Venus travel
through when its
angular displacement
is π/3 rad?
The world’s fastest
centrifuge attains an
average angular speed of
4
2.65 x 10 rad/s. What was
the centrifuge’s
angular
displacement
after 1.5 s?
The world’s largest planetarium
dome is 30 m in diameter. What
would your angular displacement be
if you ran around the perimeter of
this dome for
120 s with an
angular speed of
0.40 rad/s?
A grindstone for sharpening
knives and axes turns with an
angular speed of 10.0 rad/s. If the
tangential speed of the
grindstone’s rim is 4.60 m/s,what
is the radius of a grindstone?
A unicycle has a wheel diameter
of 40 cm. If the wheel’s average
angular acceleration was 2.0
2
rad/s , how long would it take
for the wheel’s
angular speed to
increase from 0 rad/s
to 9.4 rad/s?
A whip 0.56 m long moves in a
circle and its angular speed
increased from 6.00 rad/s to 6.30
rad/s in 0.60 s, what would the
magnitude of the
tip’s angular
acceleration be?
It’s tangential
Acceleration?
A turntable with an
2
acceleration of 1.5 rad/s
causes a record to increase its
speed to 8 rad/s over a period
of 2.5 seconds.
What was the initial
speed of the record?
A lever is used to lift a boulder.
The fulcrum is placed 1.60 m
away from the end at which you
exert a downward force,
producing a torque with a
magnitude of 400
N·m. If the angle between
the force and the lever
is 80.0°, what is the
applied force?
A force is applied to a door at
an angle of 45.0° and 1.5 m
from the hinge. What force
produces a torque with a
magnitude of 2 N•m?
How large is the
maximum torque
this force can exert?
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
F
F
1
2
net torque? θ
θ2
A
1
r1
r2
A uniform 40 N board supports two
children, one weighing 510 N and
the other weighing 350 N. The
support is under the center of mass
of the board and the 510 N child is
1.5 m from the center. Where
should the 350 N child sit to
balance the system? What is the
normal force acting on the board?
A beam of length 10 m, whose mass is
1.8 kg rests w/ its ends on 2 digital
scales. A mass (2.7 kg) rests on the
beam a distance 2.5 m from the
beam’s left end. What is the normal
force from each scale?
scale
scale
10 m
A window washer is standing
on a 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 worker
stands 1 m from the left end?
A solid disk with mass of 0.165
kg and radius 0.135 m is
spinning at a rate of 30 rad/s
and can be stopped in 0.1 s.
What is the torque needed to
cause the disk to stop in this
amount of time?
A 30 kg uniform solid cylinder
has a radius of 0.18 m. If the
cylinder accelerates at a rate of
-2
2
2.3 x 10 rad/s as it rotates
about its center, how large is
the torque acting on it?
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?
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?