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CIRCUS Study Guide: Center of Mass Page 2

Just like for normal forces, theres a simple law that tells you how much effect a torque willhave on an objects rotation:

T = I!

T is the torque, I is the objects moment of inertia, a quantity that incorporates both mass,

and distance from the pivot point. Finally, ! is the rotational acceleration that results fromthe torque.

The reason Jessica keeps her arms outstretched and leg kicked back is that these extendedlimbs act as lever arms, generating balancing torques that keep her from tipping over. A good

way to visualize how this works is to think about a seesaw.

Torque in these scenarios can be found bymultiplying:

mass x gravity x distance to the pivot

In scenario A, the torque on both sides ismgL, so the people are balanced. In

scenario B, the mass on the left side is thesame as the right side but it is at half thedistance, therefore the torque is greateron the right side and it rotates in thatdirection. In scenario C, the torque on the

left side is 2mgL and mgL on the right.Now the torques are unbalanced in theopposite direction, so the see saw rotatesthe other way. In D, the mass on the leftside is again doubled, but is only half asfar from the pivot, so the torque is half

that in C, thus the seesaw balances withno rotation.

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