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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