PHY183-Lecture28 - Torque So far in our discussion of...

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1 March 14, 2012 Physics for Scientists&Engineers 1 1 Physics for Scientists & Engineers 1 Spring Semester 2012 Lecture 28 Torque and Angular Momentum Torque So far in our discussion of forces, we have shown that forces can cause linear motion of objects We described the motion of these objects in terms of the motion of the center of mass of the object However, we have not addressed one general question: Where do we attach the force vectors acting on an extended object in a free-body diagram? You can exert a force on an extended object at a point away from its center of mass, which can cause the extended object to rotate as well as move linearly March 14, 2012 Physics for Scientists&Engineers 1 2 March 14, 2012 Physics for Scientists&Engineers 1 3 Moment Arm Consider the hand pulling on the wrench to loosen the bolt shown below Force, direction and moment arm are important Define torque as the vector cross product of the force and the moment arm Easy Not So Easy Impossible τ = r × F Torque The SI units of torque are N m The English units are foot-pounds The magnitude of the torque is Torque is an axial vector The direction of the torque is given by the right hand rule 3/14/2012 Physics for Scientists&Engineers 1 4 = rF sin θ Torque Torques around any fixed axis of rotation can be clockwise or counter-clockwise A clockwise torque tends to make an object rotate in a clockwise direction We define the net torque as the difference between the sum of all clockwise torques and the sum of all counter-clockwise torques: 3/14/2012 Physics for Scientists&Engineers 1 5 net = counter-clockwise, i i clockwise, j j Clicker Quiz Choose the combination of the position vector and the force vector that produces the highest magnitude of torque around the point indicated by the black circle. 3/14/2012 Physics for Scientists&Engineers 1 6 ABC DE = r × F
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2 March 14, 2012 Physics for Scientists&Engineers 1 7 Newton’s Second Law for Rotation We noted that the moment of inertia I is the rotational equivalent of mass Let’s consider a point particle of mass M moving around an axis at a distance R If we multiply the moment of inertia times the angular acceleration we get We can see that Which is in analogy with Newton’s Second Law I α = ( R 2 M ) = RM ( R ) = RMa = RF net F = ma τ = I Newton’s Second Law for Rotation (2) We can combine these results to get This result is for a point particle, but also holds for extended objects 3/14/2012 Physics for Scientists&Engineers 1 8 = r × F net = I Toilet Paper PROBLEM You are trying to put a new roll of toilet paper into its holder in the bathroom However, you drop the roll, managing to hold onto just the first sheet On its way to the floor, the toilet paper roll unwinds, as shown to the right How long does it take the roll of toilet paper to hit the ground, if it was released from a height of 0.73 m?
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This note was uploaded on 04/02/2012 for the course PHY 183 taught by Professor Wolf during the Spring '08 term at Michigan State University.

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PHY183-Lecture28 - Torque So far in our discussion of...

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