## Rotational Motion

##### Created by:

jenyang  on May 21, 2012

##### Description:

Circular motion, rotational mechanics, and angular momentum

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# Rotational Motion

 Circular Motionmotion with constant radius of curvature caused by acceleration being perpendicular to velocity
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#### Definitions

Circular Motion motion with constant radius of curvature caused by acceleration being perpendicular to velocity
Axis the straight line around which rotation occurs
Rotate (spin) circular motion around an internal axis (e.g. the Earth rotates to cause a cycle of day and night)
Revolve circular motion around an external axis (e.g. the moon revolves around the Earth)
Linear Speed (translational speed) the distance travelled by an object within a specified amount of time; linear speed is directly proportional to the distance an object is from the center of a rotational platform
Rotational Speed (angular speed) the speed with which an object moves through an angle for every unit of time; units: RPM (revolutions per minute), rad/s, θ/s
Period the amount of time it takes to complete one cycle (1 revolution)
Centripetal Acceleration Newton's First Law states that a body in motion stays in motion at a constant speed and in a straight line unless acted upon by a net force; therefore, a force must be pulling inward on an object moving in a circular path in order to prevent it from moving in a straight path.
Centripetal ("Center-Seeking") Force any force that acts at a right angle to a moving object's path and results in circular motion
Centrifugal ("Center-Fleeing") Force This force is not an actual force; it is a fictitious force that seems to pull outwards on an object on a circular path. This effect is due to inertia, or the tendency for a moving object to follow a straight path.
Simulated Gravity Centrifugal force can simulate gravity because from within a rotating frame of reference, there seems to be a centrifugal force directed outward.
Formula for Centripetal Acceleration a = v^2/r = 4rπ^2/T
where v = velocity, r = radius, T = period
Formula for Centripetal Force F = ma = m(v^2/r)
where m = mass, a = centripetal acceleration, v = velocity, r = radius
Torque the tendency of a force to rotate an object about an axis (force x lever arm)
Rotational Inertia the resistance of an object to changes in its rotational state of motion
Rotational Velocity (angular velocity) the rate of rotation around an axis (expressed in radians or revolutions per second/per minute)
Pendulum an object hanging from a fixed point which, when pulled back and released, is free to swing back down by gravity and inertia
Formula for Torque Torque = r x F
where r = the displacement vector, F = the force vector
Formula for Rotational Inertia I = mr^2
where m = mass, r = distance, I = rotational inertia
Angular Momentum the quantity of rotation of a body, which is the product of its moment of inertia and its angular velocity
Law of Conservation of Momentum Iiωi=Ifωf
where li = initial momentum, ωi = initial angular speed, lf = final momentum, and ωf = final angular speed
Formula for Angular Momentum L = Iω
where L (angular momentum) translates to linear momentum (p), and I (moment of inertia) translates to mass (m), and ω (angular velocity) translates to velocity (v). This is the translation from rotational (circular world) terms to linear terms (linear world).

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