Lesson 6
TORQUE AND
ROTATIONAL
EQUILIBRIUM
Announcements

Science Olympiad meets at 1:45PM
(be there Olympians and wannabe Olympians)
HW #7 due today (FR#2 Springs)
 HW #6 due tomorrow
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Exam Repair: Friday 7am, 4th, 3pm.
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Schedule of packet problems
LESSON 6:
Torque and rotational equilibrium
AP Physics B Standards

I.E.2.Torque and Rotational Statics
a) Students should understand the concept of torque, so they can:
(1) Calculate the magnitude and direction of the torque associated with a
given force.
(2) Calculate the torque on a rigid object due to gravity.
b) Students should be able to analyze problems in statics, so they can:
(1) State the conditions for translational and rotational equilibrium of a rigid
object.
(2) Apply these conditions in analyzing the equilibrium of a rigid object under
the combined influence of a number of coplanar forces applied at different
locations.
Lesson Objectives
Students will be able to:
1.
calculate the torque from an applied force and length of lever arm.
2.
use torque to model and predict rotational equilibrium.
Torque
Torque is a combination of the applied
force F, the length of the moment arm
r, and the sine of the angle between
the two, θ.
Torque

If we know the angle  between F and r, we can calculate
torque!
 = r F sin 
◦
◦
◦
◦
 is torque
r is “moment arm”
Hinge (rotates)
F is force
 is angle between F and r
r
Direction of
rotation

F
Units for Torque
The unit for torque is the Newton-meters (Nm)
Although these are the same units we used for work
(and energy), don’t confuse the concepts


Work – force along the direction of motion
(parallel)
Torque – force at a right angle to the
direction of motion (perpendicular)
Consider the door to the classroom. We use torque
to open it. Identify the following:
A. The point of rotation.
B. The point of application of force.
C. The moment arm (r).
D. The angle between r and F (best guess).
Sample Problem 6.1: A crane lifts a load. If the mass of the load is 500 kg, and the crane’s 22‐m long arm is at a 75o angle relative to the horizontal, calculate the torque exerted about the point of rotation at the base of the crane arm due to the weight.
Sample Problem 6.2: A double pulley has two weights hanging from it as shown. A) What is the net torque?
B) In what direction will the pulley rotate?
3 cm
2 cm
10 kg
2 kg
Consider a balanced situation
40 kg
ccw = cw
40 kg
This is called rotational equilibrium!
 Σ= 0 (net torque is zero)

Sample Problem 6.3: A 5.0‐meter long see saw is balanced on a fulcrum at the middle. A 45‐kg child sits all the way on one end and a 60‐kg child sits all the way on the other end. If the see saw has a mass of 85 kg, where must the fulcrum be placed to attain a balanced situation?
Sample Problem 6.4: A 10‐meter long wooden plank of mass 209 kg rests on a flat roof with 2.5 meters extended out beyond the roof’s edge. How far out on the plank can an 80‐kg man walk before he is in danger of falling?