Rotational Motion Emily Burns Molly McGeady Hung Nguyen

Definition  Rotational motion- the measure of an object that is making a circular or spinning motion.

Angular  Angular displacement  Angular displacement—change in the angle as the object rotates.  2pi(rad)  Distance given by d=r(angle)  Angular velocity  Angular velocity—angular displacement divided by the time taken to make the displacement.  W=(change in angle)/(change in time)  Angular acceleration  Angular acceleration—defined as the change in angular velocity divided by the time required to make the change.  A=(change in w)/(change in time)

Rotational Dynamics  Lever arm— perpendicular distance from the axis of rotation to the point where the force is exerted.  L=r(sin*angle)  R—distance from the axis of rotation.  Change—angle between the force and the radius from the axis of rotation to the point where the force is applied.  Torque—measure of how effectively a force causes rotation.  T=Fr(sin*change)  Torque is equal to the force times the lever arm.

The Moment of Inertia  Moment of inertia—resistance to rotation.  I=m(r^2)  The moment of inertia of a point mass is equal to the mass of the object times the square of the object’s distance from the axis of rotation.

Rotating Frames of Reference  Motion is important to us because the Earth rotates. (DUH!)  The effects of the rotation of Earth is too small to be notice in a classroom or lab.  Significant influences on the motion of the atmosphere, and therefore on climate and weather.

Centrifugal and Centripetal Force  Centrifugal force is used for two different concepts.  Centrifugal force is one of the fictitious forces that appears to act on an object when its motion is viewed from a rotating frame of reference.  Magnitude of centripetal force is F=mv2/r.  Force that maintains circular motion is centripetal force.

Coriolis Force  Coriolis effect is an apparent deflection of a moving object in a rotating frame of reference.  Centrifugal and Coriolis force are not real forces.

Newton’s Second Law for Rotational Motion  States that the angular acceleration is directly proportional to the net torque and inversely proportional to the moment of inertia.  A= T(sub net)/I  The angular acceleration of objects is equal to the net force torque on the object, divided by the moment of inertia.

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