Physics 3A: Torque & Equilibrium
Shoup โ 111
Lets talk about what causes rotational motion
We know forces cause translational motion
Another vector quantity derived from forces cause
rotational motion.
This is Torque
Consider the figure below:
We define the torque as:
We can understand this by
considering how one opens
a door
You push perpendicular to
the door, the door rotates
You push parallel to the
door, the door does not
rotate
๎
๎
r F sin
๎
(10.18)
Pushing parallel is the F cos ฯ part => doesn't produce rotation
Pushing perpendicular is the F sin ฯ part:
Another way to look at it is:
where r sin ฯ is called the
moment arm of the force
Its the perpendicular distance
from the rotation axis to the line
of action
The larger the moment arm, the larger the torque
We also define the "sign" of the torque by "+" if its resulting
rotation would be counterclockwise, and by "-" if its resulting
rotation would be clockwise.
๎
๎
F
๎
rsin
๎
๎
๎
๎
r
๎
Fsin
๎
๎
Physics 3A: Torque & Equilibrium
Shoup โ 112
๎๎๎
๎๎๎
๎๎๎
๎๎๎
๎
Consider the figure to the right:
What is the sum or the net torque?
WARNING: torque is NOT a force.
force cause torque
torque depend on the force, but also on the point of
application of the force.
Torque is a vector quantity, so we need to define its direction
Consider when I push on the bicycle wheel.
When wheel is rotating counterclockwise, we said its angular
velocity is up (right-hand rule)
Seems natural to say a torque which produces counterclockwise
rotation should also be "up"
๎
net
๎
๎
1
๎
๎
2
๎
F
1
d
1
๎
F
2
d
2
Physics 3A: Torque & Equilibrium
Shoup โ 113
If we choose this then we can define the torque mathematically as:
This is the "vector product" or
"cross product" of the vectors r
and F
The vector product of two vectors
is a vector, thus has a magnitude
and a direction
Magnitude of:
is:
The direction is given by the "right hand rule":
point fingers of right hand in direction of A (first vector)
curl fingers into B (second vector)
Thumb points in direction of C
๎๎๎
๎
๎
r
๎
๎
F
(10.10)
๎
C
๎
๎
A
๎
๎
B
C
๎
!
C
๎
"
A
"
"
B
"
sin
#
(10.21)
Physics 3A: Torque & Equilibrium
Shoup โ 114
