Transcript Welcome to PHY 1151: Principles of Physics I

Chapter 11
Rotational Dynamics and Static
Equilibrium
Dr. Jie Zou PHY 1151G
Department of Physics
1
Torque

Definition of torque, ,
for a tangential force:



Magnitude of  :  = rF.
SI units: Nm.
Tangential force: the applied
force is tangential to a circle
of radius r centered on the
axis of rotation.
Dr. Jie Zou PHY 1151G
Department of Physics
2
Exercise 11-1:

To open the door in the
figure a tangential force F
is applied at a distance r
from the axis of rotation.
If the minimum torque
required to open the door
is 3.1 N·m, what force
must be applied if r is (a)
0.94 m, or (b) 0.35 m?
Dr. Jie Zou PHY 1151G
Department of Physics
3
General definition of torque

Radial force produces zero torque and
thus causes no rotation.



Radial force: force along a line that extends
through the axis of rotation.
It is the tangential component of the
force alone that produces torque and
thus causes rotation.
General definition of torque, :


Magnitude of  = r(F sin).
 : the angle between the direction of the
force and the radial direction.
Dr. Jie Zou PHY 1151G
Department of Physics
4
Sign convention for torque

Sign convention for torque: By convention, if
a torque  acts alone, then



 >0 if the torque causes a counterclockwise
angular acceleration.
 <0 if the torque causes a clockwise angular
acceleration.
In a system of more than one torque, the sign of
each torque is determined by the type of angular
acceleration it alone would produce.
Dr. Jie Zou PHY 1151G
Department of Physics
5
Example 11-1

Two forces act on a wheel, as
shown below. The wheel is free
to rotate without friction, has a
radius of 0.42 m, and is initially
at rest. Given that F1 = 12 N
and F2 = 9.5 N, find



(a) the torque caused by F1 and
(b) the torque caused by F2.
(c) In which direction does the
wheel turn as a result of these
two forces?
Dr. Jie Zou PHY 1151G
Department of Physics
6
Torque and angular
acceleration

Newton’s second law for rotational motion:


 = net = I ,  is the total (net) torque acting,
I is the moment of inertia, and  is the angular
acceleration caused by the torque.
Analogies between rotational and linear
quantities:
Linear Quantity
m
a
F
Angular Quantity
I


Dr. Jie Zou PHY 1151G
Department of Physics
7
Moment of inertia

Definition of moment of
inertia, I:



I =  miri2.
SI units: kg·m2.
The precise value of I for a
given object depends on its
distribution of mass.
Dr. Jie Zou PHY 1151G
Department of Physics
8
Exercise 11-1:

A light rope wrapped around a diskshaped pulley is pulled with a force of
0.53 N. Find the angular acceleration of
the pulley given that its mass is 1.3 kg
and its radius is 0.11 m. (The moment
of inertia of a disk rotating about the
center axis is I = (1/2)mr2.)
Dr. Jie Zou PHY 1151G
Department of Physics
9
Static equilibrium

Conditions for static
equilibrium:


(1) The net force acting
on the object must be
zero: Fx = 0, Fy = 0,
and
(2) The net torque
acting on the object
must be zero,  = 0.
Dr. Jie Zou PHY 1151G
Department of Physics
10
Active Example 11-2

A cat walking along a uniform plank that is 4.00 m long and
has a mass of 7.00 kg. The plank is supported by two
sawhorses, one 0.440 m from the left end of the board and
the other 1.50 m from its right end. When the cat reaches
the right end, the plank just begins to tip. What is the mass
of the cat?
Dr. Jie Zou PHY 1151G
Department of Physics
11
Homework

Chapter 11, Page 341, Problems: #1, 8,
20, 35.
Dr. Jie Zou PHY 1151G
Department of Physics
12