Rotation: Worksheet 9 Newton’s Second Law for Rotation

Rotation: Worksheet 9
Newton’s Second Law for Rotation
1. The length of a bicycle pedal arm is 0.152 m , and a downward force of 111 N is
applied by the foot. Calculate the magnitude of the torque about the pivot point
when the arm makes the following angle with the vertical.
a. 30.
b. 90.
c. 180
2. A merry-go-round has a rotational inertia of 3000. kg.m2. A clockwise 2500 Nm torque
is applied to a pulley connected to the bottom of the ride. There is a 500. Nm
frictional torque in the axle. Determine the angular acceleration for the merry-goround.
3. A wheel of radius 0.20 m is mounted on a frictionless horizontal axle. A massless
cord is wrapped around the wheel and attached to a 2.0 kg box that slides on a
frictionless surface inclined at 20. with the horizontal. The box accelerates down
the incline at 2.0 m 2 .
a. Calculate the tension in the string. Draw a force diagram of the box.
b. What is the
component of the
linear acceleration
of the outside of the
c. What is the angular
acceleration of the
d. What is the rotational
inertia of the wheel
about the axle?
Rotation: Worksheet 9
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4. When a torque of 32.0 Nm is applied to a certain wheel of mass 3.25 kg , it acquires
an angular acceleration of 25.0 rad 2 .
a. What is the
b. If the wheel can be
c. What would the
rotational inertia
approximated as a
wheel’s radius be if it
of the wheel?
hoop, what is its
must be approximated
as a disk?
5. A pottery wheel, initially at rest, is assumed to be a uniform disk of mass 3.0 kg and
radius 20.0 cm. A 25.0 N force is applied tangentially to the rim.
a. Determine the
b. If the force is applied
c. What will be the
for 30.0 s, find the
angular displacement
acceleration of this
for this wheel from
instantaneous angular
t = 15 s until t = 30 s?
pottery wheel.
velocity at 30.0 s.
6. A thin spherical shell  I  MR 2  has a radius of 1.90 m . An applied torque of
960 Nm imparts to the shell an angular acceleration equal to 6.20 rad 2 about an
axis through the center of the shell.
a. What is the rotational inertia of
b. Calculate the mass of the shell.
the shell about the axis of
Rotation: Worksheet 9
7. Two blocks, each of mass m , are
suspended from the ends of a rigid,
weightless rod of length l1  l 2 , with
l1  20. cm and l 2  80. cm . The rod is held
in the horizontal position shown and then
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a. Draw a force diagram
of the rod in the position shown.
b. Find an expression for the rotational inertia of the system in terms of m, l1 , and
l 2 . (Treat the two masses as point particles located at the ends of the rod.)
c. Calculate the angular acceleration of the rod the instant it is released.
d. Calculate the linear acceleration of each block the instant they are released.
Rotation: Worksheet 9
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8. A constant force F is applied to the rightmost
ball of a two ball object, each of mass
m, connected by a massless rod. The force is applied in such a way that it always
acts perpendicular to the rod as the object rotates in the horizontal plane from rest
with no friction. Express your answers in terms of M, L, t and F only.
a. What is the
b. What torque acts on the c. What is the resulting
rotational inertia of
angular acceleration of
the object?
the object?
The object rotates for a time t.
c. What is the angular
velocity of the
rightmost ball?
d. What is the angular
velocity of the leftmost
f. What is the radial acceleration of
each ball?
e. What is the linear
velocity of each ball?
g. What is the tangential acceleration of
each ball?
Rotation: Worksheet 9
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9. A box of mass m is hung from a massless rope which is tied around a pulley that can
be approximated as a hoop of mass M and radius R as in the diagram above. The
rope does not slip.
a. Draw force
b. Compare the
c. Write Newton’s 2nd Law
diagrams of the
magnitudes of
equations for the pulley and the
box in terms of m, M, R, FT, g,
hoop and the
the forces acting
and a. You must indicate
on the box.
Justify your
directions (+ or -) for all vector
quantities using a conventional
coordinate system.
Answer the following in terms of m, M, and g only.
a. What is the acceleration of the box? b. What is the force of tension in the