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					   AP Physics       Chapter 8
Rotational Motion and Equilibrium
   Chapter 8: Rotational Motion and
              Equilibrium

8.2 Torque and Equilibrium (omit Stability)
         Homework for Chapter 8
• Read Section 8.2

• HW 8.A: p.285-286: 14, 18, 19, 20, 22, 23, 24, 26, 27, 29
8.2: Torque and Equilibrium
Warmup: Torque Your Way In                                        Physics Warmup # 71


An object rotates because a torque acts on it. When you exert a force at the end
of a wrench in order to rotate it (along with the bolt it is attached to), you may not
have thought about the fact that you applied the force perpendicular to the
handle. The longer the wrench’s handle, the less force you have to apply,
because the amount of torque is equal to the product of the force times the
distance to the axis about which it is rotating.
_________________________________________________________________

Use the relationship of torque to force and distance to explain the following two
small mysteries in your kitchen:

1. Why is it easier to open a cabinet door when the doorknob is at the end of the
   door than when it is in the middle of the door?

2. Why is a big doorknob easier to turn than a small one?
8.2 Torque and Equilibrium




τ = r F sinϕ
8.2 Torque and Equilibrium




    The sign convention for torques is as follows:
        -The torque, which rotates or tends to rotate the body clockwise (CW), is
        negative.
        -The torque, which rotates or tends to rotate the body counterclockwise
        (CCW), is positive.


•   The SI unit of torque is the N·m (newton-meter).
                                    8.2 Torque and Equilibrium




The perpendicular distance r┴ from the axis of rotation to the line of
action of a force is call the moment arm (or lever arm) and is equal
to r sin θ.
                                    8.2 Torque and Equilibrium




The same force in the opposite direction with a smaller moment arm
produces a smaller torque in the opposite direction.
                 8.2 Torque and Equilibrium
When a force acts through the axis of rotation, the torque is zero.
8.2 Torque and Equilibrium
equilibrium – a state in which things are in balance or are stable.

translational equilibrium – the sum of the forces on a body is zero
          • the body remains at rest or at constant velocity
          •  Fi = F1 + F2 + F3 + …. = 0

rotational equilibrium – the sum of torques on a body is zero
          • the body is rotationally at rest or rotates with a constant angular velocity
         •  τi = τ 1 + τ 2 + τ 3 + …. = 0


                                                                       F


          F                 F

                                                    F

The board is in translational                   The board is in translational but not
and rotational equilibrium.                     rotational equilibrium.
8.2 Torque and Equilibrium


mechanical equilibrium – when the conditions for translational and rotational
equilibrium are satisfied.
                            Fi = 0 (for translational equilibrium)
                             τi = 0 (for rotational equilibrium)

static equilibrium – the condition that exists when a rigid body remains at rest


What are some examples of static translational equilibrium?



What are some examples of static rotational equilibrium?



Problem-Solving Hint: Use the convention counter-clockwise (ccw) is positive and
clockwise (cw) is negative.
8.2 Torque and Equilibrium


 Example 8.1: The bolts on a car wheel require tightening to a torque of 90 m·N.
 If a 20 cm long wrench is used, what is the magnitude of the force required
           a) when the force is perpendicular to the wrench,
           b) when the force is 35° to the wrench as shown.
           c) Which situation requires more force, a or b? Why?
8.2 Torque and Equilibrium


 Example 8.2: A uniform board of weight 40 N supports two children weighing 500 N
 and 350 N, respectively. If the support is at the center of the board and the 500 N
 child is 1.5 m from the center, what is the position of the 350 N child?
8.2 Torque and Equilibrium


 Example 8.3: A 10 m long uniform beam weighing 100 N is supported by two ropes
 at the ends as shown. If a 400 N person sits at 2.0 m from one end of the beam,
 what are the tensions in the ropes?
8.2 Check for Understanding
8.2 Check for Understanding
8.2 Check for Understanding
8.2 Check for Understanding
8.2 Check for Understanding




 (Hint: Use worker A as the pivot point.)
8.2 Check for Understanding

             a
                    Homework 8.A

• HW 8.A: p.285: 14, 18, 19, 20, 22, 23, 24, 26, 27, 29.
End of Chapter 8

				
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