• When you want an object to turn or rotate,
you apply a torque.
• Torques produce rotation.
• Torque is produced when a force is applied
• Ex) If you want to pull a nail from a piece of
wood, the longer the handle of the hammer,
the easier of the task.
• A door knob is placed far away from the
turning axis of the hinges to provide more
• Direction of the applied force is also important
– Example, you would never pull/push the
doorknob side to side to open the door, but
instead apply the force perpendicular to the door.
Mathematics of torque
• Torque = perpendicular force * lever arm
– The same torque can be produced by a large force
with a short lever arm, or a small force with a long
• The second is better for tool application.
– Greater torques are produced when both the
force and lever are large.
• Even when weights are not equal, a seesaw
can be balanced.
• Weight alone does not produce rotation,
• How can you balance a seesaw with a large kid
on one side and a small kid on the other?
• Another application of balanced torques is
• The sliding weights are adjusted so that the
arm remains horizontal.
• Hang a meter stick so that it is balanced.
• Hang a 20g mass from the 10cm mark on the
• Where should a 100g mass be placed to
balance the meter stick?
• An object will topple if its center of gravity is
not above a support base.
• The reason for this toppling is that you now
have applied a torque around the center of
What determines how a football flies?
• First a force is required to launch the
• If all the force is through the CG, then the
football will move as a whole.
• If the force is directed “off-center”, then the
CG will be launched and also the object will
rotate about its CG
• To get a Frisbee to fly, you need to apply a
force so that the CG will move.
• To get a Frisbee to rotate, a force must applied
off axis to give it a torque.
• An object rotating about an axis tends to keep
rotating about that axis.
• There is a resistance of an object to change its
Connection to forces
• Just as it takes a force to change an object’s
linear motion, it takes a torque to change an
object’s rotational motion.
• Rotational motion depends on the mass of the
object, but also the distribution of the mass.
• The greater the distance of the bulk of the
mass from the turning axis, the more
Choking up in baseball
• A long bat is harder to bring up to speed
because the bulk of the mass is farther from
the handle (axis of rotation) than a bat you
“choke up” on.
• Long-legged animals normally run with a
slower gait for the same reason.
• Two pendulums, with the same mass are
• One has a longer string holding it than the
• Which has a faster swing?
• Why does the tightrope walker have a long
pole to help him balance?
• It is increases their rotational inertia and
makes him resist rotation over the edge of the
• Stand up and stand to the side of the lab
• Swing one leg back and forth with a straight
• Now bend the leg and swing back and forth.
• Which is easier? Why?
• Connect to running.
• Flipping your pencil back and forth.
• Hold it in near the end and try to flip the
pencil back and forth.
• Now hold it in the middle.
Rotational Inertia of a Human
• There are three principle axes of rotation for a
• Each has a different rotational inertia.
• Which way is it easiest to rotate? (in the
absence of gravity)
• How can you increase the rotational inertia of
the longitudinal axis?
• Why is it better to “tuck” if you want to get
more flips in before hitting the water if you
are a diver?
• An object that is rotating tends to continue to
rotate unless acted upon by a torque.
• The inertia of rotation is known as angular
• Angular momentum =
rotational inertia * rotational velocity
• Bicycle wheel gyroscope
• An object or system of objects will maintain its
angular momentum unless acted upon by a
• When the wheels are at rest, we fall over.
• When the wheels are moving, they have
angular momentum, and a greater torque is
required to change the direction of the
Conservation of angular momentum
• If no unbalanced external torque acts on a
rotating system, the angular momentum of
that system is constant.
• Explain the following example
• Figure skater spinning