Ch0120

# Ch0120 - Chapter 20 Torque &amp; Circular Motion 20 Torque...

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Chapter 20 Torque & Circular Motion 124 20 Torque & Circular Motion The mistake that crops up in the application of Newton’s 2 nd Law for Rotational Motion involves the replacement of the sum of the torques about some particular axis, τ , with a sum of terms that are not all torques. Oftentimes, the errant sum will include forces with no moment arms (a force times a moment arm is a torque, but a force by itself is not a torque) and in other cases the errant sum will include a term consisting of a torque times a moment arm (a torque is already a torque, multiplying it by a moment arm yields something that is not a torque). Folks that are in the habit of checking units will catch their mistake as soon as they plug in values with units and evaluate. We have studied the motion of spinning objects without any discussion of torque. It is time to address the link between torque and rotational motion. First, let’s review the link between force and translational motion. (Translational motion has to do with the motion of a particle through space. This is the ordinary motion that you’ve worked with quite a bit. Until we started talking about rotational motion we called translational motion “motion.” Now, to distinguish it from rotational motion, we call it translational motion.) The real answer to the question of what causes motion to persist, is nothing—a moving particle with no force on it keeps on moving at constant velocity. However, whenever the velocity of the particle is changing, there is a force. The direct link between force and motion is a relation between force and acceleration. The relation is known as Newton’s 2 nd Law of Motion which we have written as equation 14-1: = F h h m 1 a in which, a h is the acceleration of the object, how fast and which way its velocity is changing m is the mass, a.k.a. inertia, of the object. m 1 can be viewed as a sluggishness factor, the bigger the mass m , the smaller the value of m 1 and hence the smaller the acceleration of the object for a given net force. (“Net” in this context just means “total”.) F h is the vector sum of the forces acting on the object, the net force. o

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Chapter 20 Torque & Circular Motion 125 We find a completely analogous situation in the case of rotational motion. The link in the case of rotational motion is between the angular acceleration of a rigid body and the torque being exerted on that rigid body. = τ h h I 1 a (20-1) in which, a h is the angular acceleration of the rigid body, how fast and which way the angular velocity is changing I is the moment of inertia, a.k.a. the rotational inertia (but not just plain old inertia, which is mass) of the rigid body. It is the rigid body’s inherent resistance to a change in how fast it (the rigid body) is spinning. (“Inherent” means “of itself”, “part of its own being.”) I
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## This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.

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Ch0120 - Chapter 20 Torque &amp; Circular Motion 20 Torque...

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