Rolling motion (cont.)
Acceleration of rolling objects
Consider a round object (this
could be a cylinder, hoop, sphere
or spherical shell) having mass M,
radius R and rotational inertia I
about its center of mass (com), that rolls
without slipping down an
Rotational dynamics (cont.)
More examples
Work & Rotational Kinetic energy
Alternative interpretation for computing torque
All of us typically create torque several times a day whenever we push or pull
through a closed door. The force of the push generate
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Chapt. 11 examples Rolling (combined rotation & translation)
r
The cylinder, of mass m, radius r, rolls
from rest (without slipping) down the
incline of angle . What is its speed
after travelling distance L along the
incline?
m
vcom
L
Since the cylinder r
Rotational kinematics & dynamics (recap)
Before spring break we defined the rotational variables highlighting their
correspondence to the linear variables:
Translation
Rotation
Relation (radians!)
angular
displacement
x
linear
displacement
s = r
angular
v
Rotational motion (continued)
Last time, in considering the kinetic energy of the dumbbell rotor, we
arrived at the form of the rotational kinetic energy K 1 I2 and the
=2
concept of rotational inertia.
n
I = m i ri2
m
(small discrete masses)
i =1
Here, I
Rotational Kinematics
So far in our development of physics weve swept a major consideration
under the rug.
Weve spoken of objects and bodies in motion, considering their
displacements in position, but ignored their rotation.
For example, a ball swung on a
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PHY2048 Physics 1 Lecture Notes
Gravity
Gravity
Disclaimer: These lecture notes are meant as a study aid and not as a replacement for
the course textbook. Please report any inaccuracies to the professor.
Gravity
It is a fundamental force (along with elect
Energy
There is a fact, or if you wish, a law, governing natural phenomena that
are known to date. There is no known exception to this law; it is exact, so
far we know. The law is called conservation of energy; it states that there
is a certain quantity,
Exam 1: Wednesday, February 5th, 8:20-10:20pm.
Exam room assignments go by the first letter(s) of your LAST name:
Dont go to the wrong
room (zero on the exam)
A-C: New Physics Building (NPB) 1001
D-H: Norman Hall (NRN) 137
I-Sm: Carleton Hall (CAR) 0100
S
PHY2048 Spring 2014
HW5
Homework 5 Solutions
8P6.
We use Eq. 7-
12 for Wg and Eq. 8-
9 for U.
(a) The displacement between the initial point and Q has a vertical component of h
!
R downward (same
PHY2048 Spring 2014
HW4
Homework 4 Solutions
7P9.
By the work-
kinetic energy theorem,
1
1
1
W = K = mv 2 mvi2 = (2.0 kg) (6.0 m/s)2 (4.0 m/s) 2 = 20 J.
f
2
2
2
!
!
We note that the directions of v f and vi
PHY2048 Spring 2014
HW1
Homework 1 Solutions
1P3.
The metric prefixes (micro, pico, nano, ) are given for ready reference on the
inside front cover of the textbook (see also Table 12).
(a) Since 1 km
PHY2048 Spring 2014
HW2
Homework 2 Solutions
4P6.
To emphasize the fact that the velocity is a function of time, we adopt the notation
v(t) for dx / dt.
(a) Equation 4-
10 leads to
d
v(t ) =
(3.00t
PHY2048 Spring 2014
HW3
Homework 3 Solutions
5P36.
(a) Constant velocity implies zero acceleration, so the uphill force must equal (in
magnitude) the downhill force: T = mg sin . Thus, with m = 50 kg a
PHY2048 Spring 2014
HW6
Homework 6 Solutions
9P4.
4. We will refer to the arrangement as a table. We locate the coordinate origin at
the left end of the tabletop (as shown in Fig. 9-
37). With +x rightward
PHY 2048 Spring 2014 Acosta, Rinzler
Exam 1 Solutions
Exam 1 solutions
Note that there are several variations of some problems, indicated by choices in
parentheses.
Problem 1
!
!
!
Let vector a = 4 i + 3
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This is the master for Exam 1. The master exam has more questions than the 20 that were on your
exam. This is because some of the questions are repeated, but with different parameters and different
PHYSICS DEPARTMENT
correct answers. In your g