Torque

A Comparison

Which of the following do you think is easier to hold in place?

1 m

1 kg

1 m

1 kg

hand

hand

Why would one be easier than the other?They are the same weight.

What is Really Happening?

For the first object, there are only two forces acting on it to keep it at rest.

1 m

1 kg

hand

Fg

Fhand

Here the object is simply tryingto fall downward.

What is Really Happening? (part 2)

1 m

1 kghand

With the second object you still have only two forces.

Fg

Fhand

In this case, it is harder to hold still becauseyou are fighting two things-- the gravitational force and its torque.

In this case, the object will try to twist around the hand if it isnot allowed to fall.

This twisting effort is calleda torque.

torque

What is Torque?

Torque is a force’s ability to rotate an object. The symbol for torque is the Greek letter There are 3 factors that influence the torque around

a point: Magnitude of the force The distance the force is from the pivot point The angle the force makes with the lever arm.

The unit for torque is a Newton-Meter (Nm)

This is not the same a Joule

= F * r

1 m

1 kg

hand

Fg

Fhand

Pivot Point = hand location

Lever arm for Fg = 1 mLever arm for Fhand = 0 m

Fg is parallel to the lever arm, so it produces no torque

1 m

1 kghand

Fg

Fhand

Lever arm for Fg = 1 mLever arm for Fhand = 0 m

Pivot Point = hand location

Fhand has no lever arm so it produces no torque around the hand

= 90O

Fg does have a lever arm, and is not parallel to that lever arm.

= (98N) * (1m) = 98Nm Clockwise

= 98NmSo it does produce a torque aroundthe hand.

= F * r

Directions of Torques

Since torques try to rotate objects into a circle they have only two possible directions. Clockwise (often considered negative) Counterclockwise (often considered positive)

The signs follow the standard for measuring angles

= + = -

Net Torques

Just like multiple forces acting on an object sum up into one Net (resultant) Force. Multiple torques sum up to one net torque.

net = counterclockwise + clockwise

Remember C.C.W. = + and C.W. = -