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PHYSICS 241 -- Assignment 8
Reading: Get a “freshman physics” book and read what you need to solve the problems. It's usually in the
chapter called “Rotation”.
Problems 1-3 Due in class Thursday 11/13/2008
Remaining Problems due next Thursday 11/20/2008
IN CLASS – 11/11/2008
8-1) A disk of radius 0.2 m begins at rest and achieves a speed of 100 rpm after 10 seconds.
What is the magnitude of the total acceleration of a point on the rim of the wheel after 5 seconds?
8-2) A 2.4 kg block rests on a slope as is attached by a
string of negligible mass to a solid drum of mass 0.85 kg
and radius 5.0 cm, as show in the figure. When released,
the block accelerates down the slope at 1.6 m/s^2.
What is the coefficient of friction between the block and the
slope?
8-3) A cylinder rolls without slipping down an inclined plane of angle theta.
a) Use energy methods to calculate its velocity at the bottom of the ramp.
b) What is the linear acceleration of its center of mass?
c) Now use the rotational form of Newton's second law to calculate the acceleration of its center of mass.
8-4) Masses m1 and m2 hang on either side of a frictionless and massless pulley.
a) Derive an expression for the acceleration of the masses and the tension in the pulley.
b) Repeat this work for the case of a pulley with mass M and radius R. You may assume it is a solid
disk of uniform density. [Hint, in part “b”, there are actually two tensions to solve for].
8-5) A uniform spherical shell of mass M=4.5 kg and radius R=8.5 cm can rotate about a vertical axis on
frictionless bearings. A massless cord passes around the equator of the shell, over a frictionless pulley of
mass 1.2 kg and radius 5 cm and is attached to a small object of mass 0.6 kg. What is the speed of the object
when it has fallen 82 cm after being released from rest? [Use energy methods]
8-6) A meter stick of mass M is oriented vertically (along the y axis) on a frictionless horizontal table.
A hockey puck of mass m has an initial velocity v along the x axis. It strikes the meter stick a distance d from
its center line.
(a) What quantities are conserved in this collision?
(b) What must be the mass of the puck so that it remains at rest immediately after the collision?
[Note: A general analysis of this system, with animation and generalization to more complex shapes than
sticks would make a good project.]
