Unit 7 - Rotation and Torque

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Angular position

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θ

radians

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Angular displacement

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\
Δθ

radians

Δθ= θf - θi

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18 Terms

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Angular position

θ

radians

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Angular displacement

\
Δθ

radians

Δθ= θf - θi

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Angular velocity

rad/sec

<p>⍵</p>
<p>rad/sec</p>
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Angular acceleration

rad/s/s

<p>⍺</p>
<p>rad/s/s</p>
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Counterclockwise rotation (CCW)

+

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Clockwise rotation (CW)

-

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  • centripetal acceleration
  • tangential acceleration

An object traveling in a circle has 2 types of acceleration

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Centripetal acceleration

  • changes object’s direction of velocity
  • perpendicular to velocity
  • points toward the center
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Tangential acceleration

  • changes magnitude of object’s velocity
  • antiparallel or parallel to velocity
  • tangent to the circular path
<ul>
<li>changes magnitude of object’s velocity </li>
<li>antiparallel or parallel to velocity</li>
<li>tangent to the circular path  </li>
</ul>
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Torque

  • The ability of a force to cause angular acceleration
  • 𝜏
  • Nᐧm
  • 𝜏=rFsin(θ)
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Torque due to gravity

𝜏 = r(mg)sin(θ)

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Newton’s 1st Law for Rotation

  • net torque will change its angular velocity
  • net torque of 0 = no rotation or rotating at a constant angular velocity
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Static equilibrium

Fx=0

Fy=0

𝜏=0

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Newton’s 2nd Law for Rotation

𝜏net=I⍺

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Rotational inertia

  • property of an object
  • depends on mass and how it is distributed
  • I=mr^2
  • The further the mass is “pushed out” from the axis, the greater the rotational inertia
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s (linear position) =

θr

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v =

⍵r

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a =

⍺r

\