Torque
Force applied at a distance
causing a rotating effect
Center of Gravity
The point at which
all of the weight
of the object can
be considered to
be 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 applied
perpendicular 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 CCW
Always used
Σ Up F = Σ Down F
Not always necessary to use this
Example 1
A 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 2
Two 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.