Phys201_chapter10_part2.pdf - Torque If a net force changes...

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10/26/2017 1 If a net force changes the translational velocity, what changes the angular velocity of a rigid object? If Z is not constant, o Both angular acceleration and tangential acceleration are not zero. o A net force with a tangential component ࠵? ࠵? must act on the rigid object. Torque Torque Example: Opening a door To open a door, we must apply a force to the door. What does angular acceleration depend on? Consider the diagrams at the left. The force has the same magnitude in all three scenarios. In which scenario will the door open the most easily? Cutnell, J.D. and Johnson, K.W., 2013, Physics 9 th Edition, Wiley, Hoboken, NJ.
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10/26/2017 2 Torque Angular acceleration will be relatively large if o The force is applied far from the axis of rotation o The force is perpendicular to the door. Two components for force 1. Tangential ( F t ) 2. Radial ( F r ) Only the tangential component changes Z . Angular acceleration depends on more than just the force. Cutnell, J.D. and Johnson, K.W., 2013, Physics 9 th Edition, Wiley, Hoboken, NJ. “Torque is a turning or twisting action on a body about a rotation axis due to a force Ԧ ࠵? ” (Module 10 -6) If a force with a tangential component F t is applied at a perpendicular distance r from the axis of rotation then torque ࠵? = ࠵?࠵? ࠵? Torque relative to an axis Torque
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10/26/2017 3 Other ways to calculate torque Determine the moment arm r A and calculate torque by using ࠵? = ࠵? ࠵? F is the magnitude of the force Note: r A is also called the lever arm. Torque Two equations for torque ࠵? = ࠵? ࠵? = ࠵?࠵? ࠵? The above equations only work when calculating the torque about a fixed axis. The more general way to calculate the torque due to Ԧ ࠵? Ԧ ࠵? = Ԧ ࠵?࠵? Ԧ ࠵? S.I. unit: N m Torque
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10/26/2017 4 Direction of torque In a three dimensional case, the direction of torque is determined using the right hand rule. If the object rotates about only one axis, there are two possible directions 1. Clockwise: Negative torque 2. Counterclockwise: Positive torque Torque Net Torque Suppose multiple forces produce a torque. How do you find the net torque? The net torque on an object equals the vector sum of all the individual torques on that object. Torque is a vector o Clockwise (cw): negative o Counterclockwise (ccw): positive The net torque Σ࠵? = ࠵? ࠵?࠵?࠵? − ࠵? ࠵?࠵?
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10/26/2017 5 In a previous chapter, we said that an object was in equilibrium if no net force acts on the object. There’s an additional requirement: Net torque on the object must also be zero. If an object is in equilibrium then 1. Net force on the object is zero (constant linear velocity) AND 2. Net torque on the object is zero (constant angular velocity) Equilibrium The figure shows an overhead view of two assemblies: assembly A and assembly B. Each assembly consists of a rod with two particles attached to it. Each rod has the same length and negligible mass. A net force F A and F B is applied to assemblies A and B, respectively.
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