Rotational motion
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Rotational Motion. Rotational Motion. Rotational motion is the motion of a body about an internal axis. In rotational motion the axis of motion is part of the moving object.

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Rotational Motion

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Rotational Motion


Rotational Motion

  • Rotational motion is the motion of a body about an internal axis. In rotational motion the axis of motion is part of the moving object.

  • All of the properties of linear motion which we have discussed so far this year have corresponding rotational (angular) properties.


Rotational Motion

  • linear propertyangular property

  • distance(d) = angular displacement (θ)

  • velocity(v)= angular velocity (ω)

  • acceleration(a)=ang. accel. (α)

  • inertia (m) =rotational inertia (I)

  • force (F)=torque (τ)


Rotational Motion

  • The motion of an object which moves in a straight line can only be described in terms of linear properties. The motion of an object which rotates can be described in terms of linear or rotational properties.


Angular Displacement

  • Since all rotational quantities have linear equivalents, we can convert between them.

  • Angular displacement is the rotational equivalent of distance. To find the distance a point on a rotating object has traveled (its arc length) we need to multiply the angular displacement by the radius.


Angular Velocity

  • where angular displacement is measured in “radians”:

  • angular velocity= (angular displacement /time)

  • ω = (Δθ)/t

  • where angular velocity can be measured in radians/sec, or revolutions/sec.


Angular Velocity

  • Angular speed is the rotational equivalent of linear speed. To find the linear speed of a rotating object (its tangential speed) we need to multiply the angular speed by the radius.


Angular Acceleration

  • Angular acceleration is also similar to linear acceleration.

  • Angular acceleration=angular speed/ time

  • α = ω / t


Angular Acceleration

  • Angular acceleration is the rotational equivalent of linear acceleration. To find the linear acceleration of a rotating object (its tangential acceleration) we need to multiply the angular acceleration by the radius.


Rotational Motion

  • While an object rotates, every point will have different velocities, but they will all have identical angular velocities.

  • All of the equations of linear motion which we have discussed so far this year have corresponding rotational (angular) equations.


Rotational Motion

  • linear equation angular equation

  • v = ∆x/∆t => ω =∆ θ /∆t

  • a = ∆v/∆t =>α=∆ ω /∆t

  • vf = vi + a∆t=> ωf = ωi +α∆t

  • ∆d = vi∆t + 1/2a(∆t)2=>∆ θ = ωi∆t + 1/2α(∆t) 2

  • vf = √(vi2 + 2a∆x)=> ωf = √(ωi2 + 2a∆d)

  • F=ma=> τ=I α


Rotational Motion

  • Practice problems p. 145-147


  • An object moving at constant speed in a circular path will have a zero change in angular speed, and therefore a zero angular acceleration.

  • That object is changing its direction, however, and therefore has a changing linear velocity and a non-zero linear acceleration. It has an acceleration directed toward the center of the circle causing it not to move in a straight line.

  • This is a centripetal (center seeking) acceleration.


Centripetal Acceleration

  • This acceleration is perpendicular to the tangential (linear) acceleration.

  • All accelerations are caused by forces and centripetal acceleration is caused by centripetal force. A force directed towards the center of a circle which causes an object to move in a circular path.


Centrifugal Force

  • A centripetal force pulls an object towards the center of a circle while its inertia (not a force) tries to maintain straight line motion.

  • This interaction is felt by a rotating object to be a force pulling it outward. This "centrifugal" force does not exist as there is nothing to provide it. It is merely a sensation felt by the inertia of a rotating object


Rotational Motion

  • Practice problems p. 149-150


Rotational Inertia

  • Force causes acceleration.

  • Inertia resists acceleration.

  • Torque causes rotational acceleration.

  • Rotational inertia resists rotational acceleration.

  • τ=I α = r F

  • I = m r2


Rotational Inertia

  • Inertia is measured in terms of mass. Rotational inertia is measured in terms of mass and how far that mass is located from the axis.

  • The greater the mass or the greater the distance of that mass from the axis, the greater the rotational inertia, and therefore the greater the resistance to rotational acceleration.


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