Rotational Motion

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Rotational Motion

• Physics 1010
• Dr. Don Franceschetti
• February 17, 2006

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Guide Questions

• How does physics describe rotating bodies?
• What is centrifugal force
• What are the rotational analogues of mass,
  velocity, acceleration, force, momentum

3
Rotational Motion

• Wheels are very useful. But different parts of
  the wheel have to be moving at different speeds.
  (tangential speed)
• We can describe the motion of the wheel as a
  whole by its rotational speed (angular speed) in
  revolutions per minute or radians per second.

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Rotational Inertia

• An object rotating about an axis tends to remain
  rotating about that axis unless interfered with
  by some external torque. The property of an
  object which describes its resistance to changes
  in rotation is called its rotational inertia.
• (Why dont the parts of the object move in a
  straight line?)
• Rotational inertia depends on the distribution of
  mass around the axis.

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Rotational Inertia

• Pendulum Imr2
• Hoop about normal axis Imr2
• Solid cylinder I(1/2)mr2
• Sphere about center I(2/5)mr2

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Torque

• Is the rotational analog of force
• lever arm x force
• Where lever arm is perpendicular distance from
  axis of rotation

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Center of Mass

• Is the one point in an object that seems to move
  like a point mass,
• Sometimes called center of gravity

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Locating the center of gravity

• Center of gravity is always below point of
  support of object hanging freely.
• Center of gravity must be above area of support
  when supported from below.
• Center of gravity need not be located in object

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Centripetal force

• An object moving along a curved path must be
  experiencing a force toward the center. This is
  the centripetal force.
• The centripetal force is not caused by the curved
  motion, but causes the centripetal acceleration.
• The centripetal force can be
• Gravity (moon orbit of Earth)
• Tension (rock tied to string)
• Normal force (amusement park centrifuge)
• Friction (car going around curve)

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Centrifugal force

• When the observer is moving around a curve,
  he/she will claim to feel an outward force.
• So in the amusement park centrifuge, the force
  with which seems to push you against the the wall
  is a centrifugal force.
• If (in such a centrifuge) you toss someone a
  tennis ball, it seems to follow a curved path, as
  if responding to a centrifugal force. There is
  no reaction force to this centrifugal force
  because its not a real force.

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Artificial Gravity

• Human bodies deteriorate during extended periods
  of free fall.
• So build your space station in the form of a
  donut and make it rotate. The centrifugal
  force can function as an artificial gravity.
• Laboratory centrifuge uses same principle but at
  much higher rotational speeds.

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Angular Momentum

• Single particle moving in circle
• Angular momentum Lmvr
• Rigid body
• Angular momentum LI ?
• Greek lower case omega is angular speed
• Roman I is rotational inertia

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Conservation of Angular Momentum

• An object or system of objects will maintain its
  angular momentum unless acted on by an external
  torque.
• Angular momentum is a vector directed along axis
  of rotation (direction by right hand rule).

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Angular Momentum

• Bicycle wheels have a good bit of angular
  momentum. So its hard to fall off a moving
  bicycle.
• Ice skaters, gymnasts, and divers all make use of
  angular momentum conservation.

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Rotational Kinetic Energy

• For rotating body, KE (1/2)mv2(1/2)Iw2
• This is a design consideration for wheeled
  vehicles.
• Freight trains have small diameter wheels,
  passenger trains have bigger. Movie westerns are
  misleading.

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Flywheels

• Use rotational inertia to stabilize machines.
• Have been proposed to store kinetic energy in
  automobiles.

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Study questions

• Chapter 8 Review Questions 2, 3, 8, 9, 15, 26, 32