Download Chapter 1 Quick Review

TA: Tomoyuki Nakayama
March 1st – March 2nd, 2010
PHY 2048: Physics 1 with Calculus, Spring 2010
Review: Chapter 10.1-10.10
The purpose of this review is to refresh your memory. Physics is a cumulative subject, so make it
sure that you understand basic concepts and typical problem solving techniques in previous chapters
before moving on to a new chapter.
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A. Kinematics for Rotational Motions
A drum rotates about its central axis at an angular velocity of 20 rad/s. It then slows down with
constant acceleration. If it takes 5 s to stop, what is the number of rotation during the 5-s interval?
B. Rotational Inertia.
Four particles, each of mass 1 kg are placed at the vertices of a square with sides of
length 0.2 m. The particles are connected by rods of negligible mass. What is the
rotational inertia of the system about an axis that passes through one of the
particles and is perpendicular to the plane of the square?
C. Equation of Motion in Angular Form
A hanging block of mass 0.3 kg is attached by a massless string that
passes over a pulley and connected to another block of mass 0.4 kg on a
horizontal surface. The rotational inertia of the pulley is 2 × 10-3 kg m2
and the radius of the pulley is 10 cm. The string does not slip on the
pulley. The hanging block is released from rest. What is the acceleration
of the hanging block?
C. Rotational Kinetic Energy
A uniform rod with length of 0.5 m and mass of 2 kg is free to rotate about a pin
through one end. The rod is released from rest at angle θ = 90º. Find the angular
speed at the bottom (θ = -90º)of the motion.
TA: Tomoyuki Nakayama
March 1st – March 2nd, 2010
PHY 2048: Physics 1 with Calculus, Spring 2010
Practice Exam Problems (Chapter 10.1-10.10)
Working on this problem set is optional, but it is strongly recommended. It is highly likely that some
of these problems will appear in the exams. Do it on a weekly basis. Cramming is tiring and
sometimes it ends up in a disaster.
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1. A wheel is spinning at 27 rad/s but is slowing with an angular acceleration that has a magnitude
given by (3.0 rad/s4)t2. It stops in a time of: (Kinematics) a. 1.7 s b. 2.6 s c. 3.0 s d. 4.4 s e.
7.3 s
2. Four identical particles each with mass m are arranged in the x, y plane
as shown. They are connected by light sticks to from a rigid body. If m =
2.0 kg and a = 1.0 m, the rotational inertia of this array about the y axis is:
(Rotational Inertia) a. 4.0 kgm2 b. 12 kgm2 c. 9.6 kgm2 d. 4.8 kgm2 e.
none of these
3. A solid uniform sphere of radius R and mass M has a rotational inertia
about a diameter that is given by (2/5)MR2. A light string of length 3R is
attached to the surface and used to suspend the sphere form the ceiling. Its rotational inertia about
the point of attachment at the ceiling is: (Parallel Axis Theorem)
4. A rod is pivoted about its center. A 5-N force is applied 4 m
from the pivot and another 5-N force is applied 2m from the
pivot as shown. The magnitude of the total torque about the
pivot (in N m) is (Torque) a. 0 b. 5 c. 8.7 d. 15 e. 26
5. A small disk of radius R1 is fastened coaxially to a larger disk of
radius R2. The combination is free to rotate on a fixed axle, which is
perpendicular to a horizontal frictionless table top, as shown in the
overhead view. The rotational inertia of the combination is I. A string
is wrapped around the larger disk and attached to a block of mass m,
on the table. Another string is wrapped around the smaller disk and is
pulled with a force F as shown. The tension in the string pulling the
block is: (Equation of Motion) a. R1F/ R2 b. mR1R2 F/(I-mR22) c.
mR1R2 F/( I+mR22) d. mR1R2 F/(I-m R1R2) e. mR1R2 F/(I+ m R1R2)
6. A disk has a rotational inertia of 6.0 kg m2 and a constant angular acceleration of 2.0 rad/s2. If it
starts from rest the work done during the first 5.0 s by the net torque acting on it is: (Rotational
Kinetic Energy) a. 0 b. 30 J c. 60 J d. 300 J e. 600 J
Answers: 1-c 2-b 3-e 4-d 5-c 6-d