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Physics 111 HW13
DUE Friday, 24 June 2016
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RK01. Angles and arc lengths.
a) What angle in radians is subtended by an arc 1.50 m in length on the circumference of a
circle of radius 2.50 m? What is this angle in degrees?
b) An arc 14.0 cm in length on the circumference of a circle subtends an angle of 128o. What
is the radius of the circle?
c) The angle between two radii of a circle with radius 1.50 m is 0.700 radians. What length
of arc is intercepted on the circumference of the circle between the two radii?
RK02. A child is pushing a merry-go-round. The angle through which the merry-go-round has
turned varies with time according to θ(t) = γ t + β t3, where γ = 0.400 rad/s and β = 0.0120
rad/s3.
a) Calculate the angular velocity of the merry-go-round as a function of time.
b) What is the initial value of the angular velocity?
c) Calculate the instantaneous value of the angular velocity ω at t = 5.00s and the average
angular velocity ωavg for the time interval t = 0 to t = 5.00 s. Show that ωavg is not equal to
the average of the instantaneous angular velocities at t = 0 and t = 5.00s, and explain why
it is not.
d) Determine αavg for the time interval t = 0 to t = 5.00 s.
RK07. An electric ceiling fan with blades 0.750 m in diameter is rotating about a fixed axis with
an initial angular velocity of 0.250 rev/s. The angular acceleration is 0.900 rev/s2.
a) Compute the angular velocity after 0.200s.
b) Through how many revolutions has the blade turned in this time interval?
c) What is the tangential speed of a point on the tip of the blade at t = 0.200s?
d) What is the magnitude of the resultant acceleration of a point on the tip of the blade at t =
0.200s?
RK08. At t = 3.00 s a point on the rim of a 0.200-m-radius wheel has a tangential speed of 50.0
m/s as the wheel slows down with a tangential acceleration of constant magnitude 10.0 m/s2.
a) Calculate the wheel’s constant angular acceleration.
b) Calculate the angular velocities at t = 3.00 s and t = 0.
c) Through what angle did the wheel turn between t = 0 and t = 3.00 s?
d) At what time will the radial acceleration equal g?
T00B. Weakman isn’t very strong. He can only apply a maximum force of 100 N to anything.
He-man is strong, and can apply a maximum force of 10000 N to anything. Is it possible for
Weakman to exert a greater torque on an object than He-man? Explain.
(over)
T00C.
Calculate the torque (magnitude and
direction) about point O due to the force F in each
of the situations sketched in the figure at right. In
each case, the force F and the rod both lie in the
plane of the page, the rod has a length 4.00 m, and
the force has magnitude F = 10.0 N.
T00D. A square metal plate 0.180 m on each side is pivoted about an
axis through point O at its center and perpendicular to the plate (see
figure at right). Calculate the net torque about this axis due to the
three forces shown in the figure if the magnitudes of the forces are F1
= 18.0 N, F2 = 26.0 N, and F3 = 14.0 N. The plate and all forces are
in the plane of the page.
T00E. A weekend plumber, unable to loosen a pipe fitting, slips a piece
of scrap pipe (a “cheater”) over his wrench handle. He then applies
his full weight of 900 N to the end of the cheater by standing on it.
The distance from the center of the fitting to the
point where the weight acts is 0.80 m, and the
wrench handle and cheater make an angle of 19o
with the horizontal (see figure). The pipe has a
diameter of 6 cm.
a) Find the magnitude and direction of the
torque he applies about the center of the
pipe fitting.
b) If the fitting doesn’t budge, what is the
frictional torque?
c) If the µs between the fitting and the pipe is
0.5, determine the normal force between the fitting and the pipe.
(over)