Download Tangential force

Chapter 11
Rotational Dynamics and Static
Equilibrium
Dr. Jie Zou PHY 1151G
Department of Physics
1
Outline
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Torque
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Torque for a tangential force
General definition of torque
Sign convention for torque
Dr. Jie Zou PHY 1151G
Department of Physics
2
Torque in everyday life
Dr. Jie Zou PHY 1151G
Department of Physics
3
Definition of torque, , for a
tangential force
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Tangential force: An applied
force that is tangential to a
circle of radius r centered on
the axis of rotation.
For a tangential force,
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 = rF
SI units: Nm
F: magnitude of the force
r: distance from the axis of
rotation to the force
Dr. Jie Zou PHY 1151G
Department of Physics
4
Example

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
5
Radial and tangential components
of force
Only tangential
component
produces torque.
A radial force
produces zero
torque.
Dr. Jie Zou PHY 1151G
Department of Physics
6
General definition of torque, 
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In general,
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 = r(F sin)
: the angle of the force
relative to the radial direction.
Two special cases:
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(1) For a radial force, =0,
and =r(F sin 0)=0;
(2) For a tangential force,
=/2, and =r(F sin /2)=rF.
Dr. Jie Zou PHY 1151G
Department of Physics
7
The moment arm, r
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The moment arm, r: The
perpendicular distance from
the axis of rotation to the line
of the force is defined to be
r .
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r = r sin
SI unit: m
Torque is the moment arm
times the force:
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 = r(F sin) = (r sin)F = rF
Dr. Jie Zou PHY 1151G
Department of Physics
8
Sign convention for torque
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Sign convention for torque: If a
torque  acts alone, then
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 >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. The net torque
acting on the system is the sum of
each individual torque, taking into
account the proper sign.
Dr. Jie Zou PHY 1151G
Department of Physics
9
Example

Two helmsmen exert the
forces shown below on a
ship’s wheel. The wheel has a
radius of 0.74 m, and the two
forces have the magnitudes
F1 = 72 N and F2 = 58 N.
Find
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(a) the torque caused by F1
(b) the torque caused by F2
(c) In which direction does the
wheel turn as a result of these
Dr. Jie Zou PHY 1151G
two forces?
Department of Physics
10
Homework

See online homework assignment on
www.masteringphysics.com
Dr. Jie Zou PHY 1151G
Department of Physics
11