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Unformatted text preview: Chapter 12 Chapter 12 Rotational Dynamics Rotational Dynamics Chapter 13 Chapter 13 Rotational Vectors Rotational Vectors Angular Momentum Angular Momentum Rotational Dynamics Rotational Dynamics The knowledge of a body’s moment of inertia allows us to use the rotational analog of Newton’s second law to determine the object’s behavior. A cylindrical satellite of radius R is spinning at a frequency f . It must be stopped so that a space shuttle crew can make repairs. Two small jets each with a thrust F are mounted tangent to the satellite’s surface as shown. How long must they fire to bring the satellite to rest? ote that the moment of inertia for a ylinder is the same as that for a disk! Does this result make sense? Δ t and 2 RF Δ 2 f I t 2 RF I t t 2 fMR 2 /2 2 RF fMR 2 F Example: Rotational Dynamics Example: Rotational Dynamics A solid cylinder of mass M and radius R is used to support a massless rope and a bucket of mass m . Find the rate of acceleration of the bucket into the well. First consider the free body diagram for the bucket: Next the free body diagram for the cylinder. The tangential acceleration of the cylinder must equal a . mg − T ma a R I R TR 2 MR 2 /2 2 T M Example: Rotational Dynamics Example: Rotational Dynamics A solid cylinder of mass M and radius R is used to support a massless rope and a bucket of mass m . Find the rate of acceleration of the bucket into the well. Substituting for T to solve for a : Note that the acceleration is reduced due to the rotational inertia of the cylinder. a 2 T / M 2 m g − a / M → a 1 2 m M 2 m M g a 2 m M 2 m g Does this result make sense? Example: Atwood Machine (again) xample: Atwood Machine (again) Now find the acceleration for the masses in an Atwood machine with a cylindrical pulley of radius R and a moment of inertia I ....
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 Spring '08
 Hicks
 Angular Momentum, Inertia, Momentum, Moment Of Inertia, solid cylinder, Rotational Dynamics

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