Rotational Motion

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# Rotational Motion - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about ' Rotational Motion' - arthur-murray

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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 property angular 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.