TorqueForce applied at a distance

causing a rotating effect

Center of Gravity

The point at whichall of the weightof the object canbe considered tobe concentrated

All measurements are made to the center of gravity

Torques

The “torque arm” must always be measured perpendicular to the direction of the force.We will only be studying torques appliedperpendicular to the bar.

Translational Equilibrium• All forces are balanced

• There is no linear acceleration

• The way we use this with rotary motion is we say:

• “The Up Forces equal the Down Forces”

• These forces are “coupled”: they do not need to act on the same point, just on the same plane

Translational Equilibrium

• If the up forces = the down forces, then

• Fa = Fb and the bar will not have a tendency to change its linear motion

Rotational Equilibrium

• Clockwise Torques = Counterclockwise Torques• Must be true about any pivot point• Therefore, in doing torque problems, choose a

pivot point that eases calculation

Summarizing Problem Solving Strategy:

Σ CW = Σ CCWAlways used

Σ Up F = Σ Down FNot always necessary to use this

Example 1A nonuniform bar is 4.5 m long and weighs 640 N. It is balanced when a 270 N weight is hung 0.80 from the light end of the bar and the bar is pivoted at the center. Where is the center of gravity of the bar? ANS: 1.6 m from heavy end

Example 2Two workers carry a nonuniform beam weighing 730 N. The beam is 2.6 m long and its center of gravity is 1.1 m from one end. If the workers hold the beam at its ends, how much does each worker lift? ANS: 310 N and 420 N

Practice Problems:

A nonuniform bar is 3.8 m long and has a weight of 560 N. The bar is balanced in a a horizontal position when it is supported at its geometric center and a 340 N weight is hung 0.70 m from the bar’s light end. Find the bar’s center of gravity. ANS: 1.2 m from heavy end

A large wooden beam weighs 820 N and is 3.2 m long. The beam’s center of gravity is 1.4 m from one end. Two workers begin carrying the beam away. If they lift the beam at its ends, what part of its weight does each worker lift? ANS: 460 N and 360 N.