SP221/2141&4341
Chapter 9 Homework
Due Monday November 14, 2016
Question 1: A child with mass m=45 kg sits at the edge of a merry-go-round with radius 1.2 m.
Starting from rest at time t=0, the merry-go-round is rotated counter-clockwise with a constant
angular acceleration of α=+0.18 rad/s2 . The coefficient of static friction between the child and the
merry-go-round is 0.040. At what time does the child slip off of the merry go round? [10 points]
Question 2: A thin plate with total mass M =1.50 kg is shown below. It consists of a circle of
diameter 10.0 cm (5.00 cm radius) in which a hole of 5.00 cm diameter (2.50 cm radius) has been
cut. What is the moment of inertia for this plate about a perpendicular axis passing through its
center? [Hint: First calculate the moment of inertia for a solid plate with the same mass density
as this object (i.e. determine what the moment of inertia was before the hole was cut in it). Then
calculate the moment of inertia for a 5 cm diameter plate, also with the same mass density, located
where the hole is (i.e. determine the moment of inertia for the piece that gets cut out). The moment
of inertia of this object will be the difference between those two answers.] [10 points]
5.0 cm
10.0 cm
Axis of rotation
(Out of page)
SP221/2141&4341
Chapter 9 Homework
Due Monday November 14, 2016
Question 3: A thin disk of radius R=0.240 m and total mass M =0.188 kg has a radially varying
density. The area mass density (mass per unit area) of the disk can be expressed as σ = Cr2 , where
the constant C=36.0 kg/m4 and r is the radial distance from the center of the disk. What is the
moment of inertia for this disk when it is rotated about its central axis? [Reminders: dm = σdA,
and the differential area in polar coordinates can be expressed as dA = r drdφ. Tip: You don’t need
to use the total mass, M =0.188 kg, to determine the answer. But you know that if the mass were
spread evenly over the entire circle the moment of inertia would be I = 21 M R2 , while if all the mass
were at the circumference (a hoop) the moment of inertia would be I = M R2 . The answer to this
problem should be somewhere between those two bounds.] [10 points]
Question 4: A unicyclist is riding her unicycle along flat ground. The wheel rolls without slipping.
The total mass of the unicyclist plus the unicycle is m=85 kg. The unicycle wheel has a radius of
R=0.18 m and a moment of inertia of I=0.75 kg·m2 . She is accelerating in the positive-x direction
with a=0.80 m/s2 . What is the magnitude of the torque that must be applied by the unicyclist to
the wheel to maintain this acceleration? [Note: this is not the same as the net torque acting on the
unicycle wheel.] [10 points]
SP221/2141&4341
Chapter 9 Homework
Due Monday November 14, 2016
Question 5: (Tipler & Mosca Problem 9-92) Released from rest at the same height, a thin spherical
shell and solid sphere of the same mass m and radius R roll without slipping down an incline through
the same vertical drop H (Figure 9-64). Each is moving horizontally as it leaves the ramp. The
spherical shell hits the ground a horizontal distance L from the end of the ramp and the solid sphere
hits the ground a distance L0 from the end of the ramp. Find the ration L0 /L. [10 points]
Question 6: A spool of string with mass M and radius R is unwound along a horizontal surface as
one end of the string is pulled horizontally with a constant tension T . Assume that the spool is a
uniform solid cylinder, that the spool rolls without slipping, and that neither the mass nor radius of
the spool change appreciably as the string unwinds. Give your answers in terms of only L and T .
(a) What is the static frictional force from the floor acting on the spool? Give both the magnitude
and direction of this force. (b) What is the total kinetic energy of the spool when its center of mass
has travelled a horizontal distance L? [10 points]
T