# Torque

```Houston…we have a problem
 1) You learned that if you push on a door far away from
it’s hinges (the axis of rotation) it will be easier to
open and close
 2) You learned if you hang a mass farther away from
your hand (the axis of rotation) it was harder to move
up and down
 Don’t they contradict one another?
So what exactly did we learn?
 The direction that you apply the force is rather
important
 If you apply your force in the same direction as the
object moves… less effort is needed with a longer lever
 If you apply your force opposite the direction that the
object moves…more effort is needed with a longer
lever
What is torque?
 Torque is a tendency of a force to rotate an object
 A force applied to an extended object can produce a
torque.
 This torque in turn causes the object to rotate.
The object rotates about an axis.
The lever arm is the distance (in meters) from
the axis of rotation to the point where the force
acts.
The applied force is the force applied to the
lever arm.
Formula For Calculating Torque
Torque = (force perpendicular to axis)(length of lever arm)
τ = Fl d
τ = the Greek Letter Tau
Fl = Force perpendicular to lever arm
d = length of lever arm.
Calculating torque
 The torque (τ) the Greek Letter Tau, created by a force
is equal to the lever arm (r) times the magnitude of the
force (F).
You try…
 A force of 50 newtons is applied to a wrench that is 30
centimeters long.
 Calculate the torque if the force is applied
perpendicular to the wrench so the lever arm is 30 cm.
You try…
 Now lengthen the arm

of the wrench to 0.7 m
τ=rxF
= 0.3 m x 50 N
= 15 N-m of Torque
You try…
 If the doorknob was
placed in the middle of a
door, rather than at the
edge..how much more
force would be needed to
produce the same torque
for opening the door?
 Twice as much
Balanced (Net) Torque
 The net torque is the
sum of all the torques
produced by all the
forces
 Net-torque is zero or..
the torques are balanced
 Counterclockwise
torque = clockwise
torque
Balanced (Net) Torque
 Equation
Fleft x rleft = Fright x rright
Calculate using equilibrium
 A boy and his cat sit on a
seesaw.
 The cat has a mass of 4
kg and sits 2 m from the
center of rotation.
 If the boy has a mass of
50 kg, where should he
sit so that the see-saw
will balance?
 A boy and his cat sit on a seesaw. The cat has a mass of 4
kg and sits 2 m from the center of rotation. If the boy has
a mass of 50 kg, where should he sit so that the see-saw
will balance?
Less force is required farther out from the center of mass than closer in.
So, by tackling a runner low -- far from the center of mass -- it takes less
force to tackle him than if he were tackled high. Furthermore, if a runner
is hit exactly at his center of mass, he will not rotate, but instead will be
driven in the direction of the tackle.
Similarly, coaches often advise linemen to stay low. This brings their
center of mass closer to the ground, so an opposing player, no matter
how low he goes, can only contact them near their center of mass. This
makes it difficult for an opposing player to move them, as they will not
rotate upon contact. This technique is critical for a defensive lineman in
defending his own goal in the &quot;red&quot; zone, the last 10 yards before the
goal line.
```