rot3 - Physics 53 Rotational Motion 3 Sir, I have found you...

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Physics 53 Rotational Motion 3 Sir, I have found you an argument, but I am not obliged to Fnd you an understanding. — Samuel Johnson Angular momentum With respect to rotational motion of a body, moment of inertia plays the same role that mass plays in the translational motion of a particle. It measures the intrinsic reluctance of a body to have its state of rotation changed. Torque plays the role in rotation that force plays in the translational motion of a particle. It describes the external inFuence that causes changes in the state of rotation. But what describes “the state of rotation” itself? ±or a particle, the state of translational motion is described by the linear momentum, p = m v . The corresponding quantity for rotational motion is the angular momentum . Like torque, angular momentum has meaning only with respect to some speci²ed reference point. Also like torque, its magnitude depends on the distance from that point. We begin with the simplest system, a single particle. Later we will generalize to systems of particles, with special interest in rigid bodies. The de²nition for a particle is: Angular momentum of a particle L = r × p Here r is the position vector of the particle relative to the reference point, and p = m v is its linear momentum. Some properties of L : L is a vector, perpendicular to the plane containing r and p , and thus perpendicular to both r and p . L is zero if the particle moves along the line of r , i.e., directly toward or away from the reference point. PHY 53 1 Rotations 3
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The magnitude is given by L = r p , where r is the moment arm , defned to be the perpendicular distance From the reFerence point to the line along which the particle moves . Alternatively, L = rp , where p is the component oF p perpendicular to r . L is a maximum, equal to rp , iF p is perpendicular to r . This is the case iF the particle moves (at least momentarily) in a circle about the reFerence point. Like linear momentum and kinetic energy, angular momentum is an important aspect oF the state oF motion oF a particle, especially oF orbital motion around some center oF Force. It is also an important property oF the behavior oF a system oF particles. Torque as a vector Here is the general defnition oF the torque oF a Force about a given reFerence point: Torque τ = r × F Here r specifes the location, relative to the reFerence point, oF the point at which the Force F is applied. Some properties oF τ : Torque is a vector, perpendicular to the plane containing r and F , and thus perpendicular to both r and F . The torque is zero iF F acts along the line oF r , i.e., directly toward or away From the reFerence point. The magnitude is given by the two Formulas introduced earlier:
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This note was uploaded on 10/19/2011 for the course PHYSICS 53L taught by Professor Mueller during the Spring '07 term at Duke.

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rot3 - Physics 53 Rotational Motion 3 Sir, I have found you...

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