Statics
Rotation, Torques and The Conditions for
Equilibrium
Conditions for Equilibrium
Q: How do you know when a body is in
equilibrium? What two distinct kinds of motion
can a body have when it is not in “balance”?
A: The body neither accelerates linearly or
rotationally. This means that:
Example: teeter-totter
• A 4 m long teeter-totter is
hinged in the middle. A 40 kg
child sits at one end, 1.75 m
from the center. Where should
a 60 kg child sit at the other
end so that equilibrium is
maintained?
• Describe the motion of the
system if the 60 kg child sat at
the extreme end, 2 m from the
center.
Basic Definition of Torque
• Torque (finally we get some direction!)
 rF
• Use the Right-Hand-Rule to determine the
direction of Torque.
Curl the fingers of your right hand in the same direction that the object spins - your
thumb points in the direction of the angular velocity, angular momentum, torque,
acceleration, displacement ….
Calculating Torques – the Cross
Product
𝑎
× 𝑏𝑏
𝑎
𝑏
−
𝑎𝑧𝑏𝑦
𝑎𝑥
𝑦
𝑧
𝑥
𝑎𝑦 × 𝑏𝑦 = 𝑎𝑧𝑏𝑥 − 𝑎𝑥𝑏𝑧
𝑎𝑧
𝑎𝑥𝑏𝑦 − 𝑎𝑦𝑏𝑥
𝑏𝑧
𝑎 × 𝑏 = 𝑎𝑏 sin 𝜃
Sample Calculation…
Practice…
• Do this in algebraic form
• Do this in polar form
A Hanging Mass
• A 5 kg mass hangs from a
cord of negligible mass.
– What is the tension in the
cord?
– The mass is pulled sideways,
deflecting the supporting cord
300 from vertical. Draw an
FBD for this case.
– Set up equilibrium conditions
using column vector format.
– How will the tension change
in the supporting cord.
Explain why this happens.
Click here to run this applet
The Human Arm
• Lets apply what we
now know to
understand the
enormous tension
forces our muscles
must be able to
withstand.
(see Example 9.4, pg331)
Man on the Ladder
• Under what
conditions is it safe to
mount a ladder?
– Use the applet on the
right to explore this
– Examine the FBD for
this system
– Use column-vector
notation!