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AP Physics Chapter 8.1 Notes TORQUE The tendency of a force to rotate a body about some axis is measured by a quantity called the torque. We can find the magnitude of the torque by using the formula: τ = Fd where τ is the torque, d is the distance of the lever arm, and F is the force. The lever arm is the perpendicular distance from the axis of rotation to a line drawn along the direction of the force. EXAMPLE: 1.0 m d2 F1=500 N d1 Question: Find the net torque exerted on the crate if its width is 1.0 m. Assume an axis of rotation is through the center of the crate. O F2=500 N Solution: The torque produced by F1 is τ1 = F1d1 = -(500N)(0.50m) = -250 Nm *A top view of a packing crate being pushed with equal but opposite forces. and the torque produced by F2 is τ2 = F2d2 = -(500N)(0.50m) = -250 Nm Because each force produces clockwise rotation, the torques are both negative. Thus, the net torque is -500 Nm. Chapter 8 Section 2 Torque and the Second condition for Equilibrium: First Condition of Equilibrium: object has no net external force acting on it. ∑F x = 0 and ∑Fy = 0. With the First condition we found that the object would stay at rest or move at a constant velocity, yet this condition doesn’t truly guarantee that an object is in equilibrium. There is a second factor or condition that needs to be fulfilled, the Second Condition for Equilibrium. The Second condition for Equilibrium: if an object is in rotational equilibrium, the net torque on it about any axis must be zero. ∑τ = 0. Now we know that a body/object in static equilibrium must satisfy two conditions: 1. The resultant external force must equal zero. ∑Fnet = 0 2. The resultant torque must equal zero. ∑τ = 0. F1 = 500N An example to better clarify: In this example we satisfy the First Condition of Equilibrium because there are equal and opposite forces acting on the crate. Although Crate the two forces are equal and opposite they are not acting on the crate trough a common point. Because of this irregularity the crate will spin. F2 = 500N Position of Axis When having to choosing an axis of rotation for calculations, the location of the axis is subjective, that is if the object in question is in equilibrium.