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Chapter 8 Additional Notes Extra Example 1: a) Calculate the net torque about the axle of the wheel. Assume that a frictional torque of 0.3 Nm opposes the motion. b) What is the angular acceleration?

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R R /2 M = 2 kg F 3 = 20 N F 2 = 30 N F 1 = 35 N From the forces, we can see that both force 1 and force 3 will rotate the wheel CW while force 2 rotates the wheel CCW. So the torque should also be CCW. a) The net torque on the wheel is then
τ = RF 2 + f R 2 F 1 RF 3 = R 2 F F 3 F 1 2 + f = 1.2 Nm The negative sign here means that the wheel will rotate in the CW direction. b) To find the angular acceleration we use the second definition of torque = I α

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Solving for the angular acceleration then gives α = τ I Here we take the wheel to be a solid cylinder, so the moment of inertia is I = 1 2 MR 2 So we have = I = 30 rad / s 2
What is the speed of mass 2 before it hits the ground? m

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