Rotational Dynamics

Moment of Inertia


<div class="wp-block-create-block-problemblock">A uniform disk is mounted to an axle and is free to rotate without friction.  A thin uniform rod is rigidly attached to the disk so that it will rotate with the disk.  A block is attached to the end of the rod.  Properties of the disk, rod, and block are as follows.<br /><img src=/old/images/momentofinertia.gif alt="physics moment of inertia problem ><br />Disk: mass = 3m, radius = R, moment of inertia about center ##I_D## = ##\frac{3}{2}mR^2##<br />Rod: mass = m, radius = 2R, moment of inertia about one end ##I_R## = ##\frac{4}{3}mR^2##<br />Block: mass = 2m<br />The system is held in equilibrium with the rod at an angle ##\theta_0## to the vertical as shown above, by a horizontal string of negligible mass with one end attached to the disk at the other to a wall.  Express your answers to the following in terms of m, R, ##\theta_0## , and g.<br />A. Determine the tension in the string<br />The string is now cut and the disk rod block system is free to rotate<br />B. Determine the following for the instant immediately after the string is cut<ul><li>The magnitude of the angular acceleration of the disk</li><li>The magnitude of the linear acceleration of the mass at teh end of the rod</li></ul><img " src="/old/images/momentofinertia2.gif"  alt="physics moment of inertia problem ><br />As the disk rotates the rod passes the horizontal position shown above<br">C.  Determine the linear speed of the mass at the end of the rod for the instant the rod is in the horizontal position.</div>


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