SP221/2141&4341
Chapter 10 Homework
Due Monday November 21, 2016
Question 1: Two pucks, each with m=1.0 kg, are attached by a string. One puck rotates in a circle
on a frictionless surface; the string passes through a hole in this surface and supports the other
puck. Initially, the first puck rotates in a circle of radius ri =0.500 m at a speed of vi =1.28 m/s
while the hanging puck is supported to remain motionless. The hanging puck is released, and it
falls. How far does this hanging puck fall before it is instantaneously comes to rest again? [Hint: as
the hanging puck falls, the rotating puck will speed up as the radius of its rotation shrinks. You will
end up with a cubic equation and therefore three solutions. Of those three solutions, I’m looking
for the one that is neither trivial nor nonsensical.] [10 points]
ri =0.500 m
Question 2: A puck of mass m rotates at a constant speed in a circle of radius r on a horizontal table.
The puck is attached to a string that leads to a frictionless hole at the center of the circle. (a) What
is the magnitude of the tension in the string? Do not use v in your answer, but you can use the
puck’s angular momentum L. (b) Suppose that the puck is initially rotating in a circle with radius
ri . The string is then gently pulled until the puck is moving in a circle of radius rf . What was the
change in the puck’s kinetic energy? Again, do not use any speed in your answer, but you may use
the puck’s angular momentum. (c) Using you answer from part a, integrate F~ · d~l to determine the
work done on the puck by the string and show that it is identical to the answer in part b. [Signs in
radial integrals can be difficult. I would note that the differential displacement is given by d~l = dr r̂
and the tension will always point in the −r̂ direction (towards the center of the circle).] [10 points]
Question 3: A merry-go-round at the playground has a radius of R=1.0 m and a moment of inertia
of I0 =35 kg·m2 . The merry-go-round is rotating about a frictionless axle with an angular speed of
ω0 =0.80 rad/s while a child of mass m=18 kg sits at its center. The child then crawls to the edge
of the merry-go-round; she does not slip. (a) What is the angular speed of the merry-go-round after
the child crawls to the edge? (b) Suppose that the child crawls outward at a uniform speed and that
it takes her 4.0 s to reach the edge: i.e. the rate of change for the child’s radial distance from the
=0.25 m/s. What is dω
, the instantaneous rate of change of the
center is constant and given by dr
dt
dt
angular speed at the moment when she is just about to reach the edge? (c) What is the magnitude
of the tangential component of the frictional force between the child and merry-go-round at this
instant? [10 points]
SP221/2141&4341
Chapter 10 Homework
Due Monday November 21, 2016
Question 4: (Tipler & Mosca Problem 10-82) (a) Assuming Earth to be a homogenous sphere that
has a radius r and a mass m, show that the period T (time for one daily rotation) of Earth’s rotation
about its axis is related to its radius by T = br2 , where b = (4/5)πm/L. Here L is the magnitude of
the spin angular momentum of Earth. (b) Suppose that the radius r changes by a very small amount,
∆r, due to some internal cause, such as thermal expansion. Show that the fractional change in the
period ∆T is given approximately by ∆T /T = 2∆r/r. (c) By how many kilometers would r need
to increase for the period to change by 0.25 d/y, (so that leap years would no longer be necessary)?
[5 points]
Question 5: (Tipler & Mosca Problem 10-84) As indicated in the text, according to the Standard
Model of Particle Physics, electrons are pointlike particles having no spatial extent. (This assumption has been confirmed experimentally, and the radius of the electron has been shown to be less
than 10−18 m). The intrinsic spin of an electron could in principle be due to its rotation. Let us
check to see if this conclusion is feasible. (a) Assuming that the electron is a uniform sphere whose
radius is 1.00 × 10−18 m, what angular speed would be necessary to produce the observed intrinsic
angular momentum of ~/2? (b) Using this value of the angular speed, show that the speed of a
point on the “equator” of a “spinning” electron would be moving faster than the speed of light.
What is your conclusion about the spin angular momentum beign analogous to a spinning sphere
with spatial extent? [5 points]
Note on questions 4 and 5: The radius of the earth, RE , is given is the Terrestrial and Astronomical Data table at the start of your textbook. The mass of an electron, me , Planck’s constant
divided by 2π, ~, and the speed of light, c, are all given in the Physical Constants table at the back
of your textbook.