Rotational Mechanics

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					Rotational Mechanics
• When you want an object to turn or rotate,
  you apply a torque.
• Torques produce rotation.
• Torque is produced when a force is applied
  with “leverage”.
• 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
  for torque.
  – 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
• Conceptually
  – The same torque can be produced by a large force
    with a short lever arm, or a small force with a long
    lever arm
     • 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,
  torque does.
• How can you balance a seesaw with a large kid
  on one side and a small kid on the other?
            Balanced Torques
• Another application of balanced torques is
  scale balances.
• 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
  meter stick.
• 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.
            Rotational Inertia
• An object rotating about an axis tends to keep
  rotating about that axis.
• There is a resistance of an object to change its
  rotational motion.
          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
  rotational inertia.
        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?
            Tightrope walker
• 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?
          Angular Momentum
• 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
  angular momentum.
 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

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