Rotational Mechanics

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Rotational Mechanics
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Torque

• Causes rotation, more specifically causes changes
  in rotation
• Its like the quantity Force but for rotation
• Torque (t) Force (F) x Lever Arm (d)Torque
  F x d
• Lever arm (d) - distance from axis of rotation
  that the F is applied
• The more torque the faster something will rotate
• View from above of Doors seen below.
• F
  F F

Good, long lever arm
Not as Good, shorter lever arm
Very Bad, no lever arm
d
d
d
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• No Force that is acting directly toward the axis,
  or directly away from it, can cause a torque

F
F
NO TORQUE, Force must be perpendicular to the
radius to cause a rotation
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Balanced Torques

• If more than one torque is acting on an object,
  the torques must be balanced on either side of
  the axis of rotation in order to be in rotational
  equilibrium (not rotating)
• In picture, axis is the triangle, Forces on
  either side of axis are not balanced. BUT
  Torques are balanced.
• Rotational Equilibrium ? Net torque 0
• Boy - Torque 500 N x 1.5 m 750 Nm
• Girl - Torque 250 N x 3 m 750 Nm
• So teeter-totter is balanced!!
• (Aka in Equilibrium)
• In this case the forces
• causing torque or the childrens
• Weight

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• Below weights hanging on a meter stick. Meter
  stick is suspended from the 50 cm mark. What is
  the weight of the first block, if the meter stick
  is balanced??
• If balanced that means that Torques on either
  side of Axis are balanced (hint-50 cm mark is
  axis)
• 20 N block --- Torque F x d 20 N x
  30 cm 600
• Unknown block -- Torque F x d ? x 40
  cm 600
• So solve for ? By dividing 600 by 40 And
  you get 15 N!!!

Dist. From axis
Dist. From axis
? 15 N
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What does COG have to do with Torque??

• Forces applied directly to the COG, have no lever
  arm.. And therefore produce no Torque.
  Meaning no rotation
• Another Football related example
• How do you kick a football so it rotates end over
  end??

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Hewitt Program