# rot - Rotational Dynamics Objective To investigate the...

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Rotational Dynamics Objective: To investigate the behavior of a rotating system subjected to internal torques and external torques. To apply knowledge gained from the linear momentum lab to its rotational analog. To see how total energy is a function of linear and rotational energy by Apparatus: Angular motion sensor, circular aluminum disc with pulleys of varying diameter on other side, meter stick, 20g mass on a string, flexible goose neck mass. Introduction: A few weeks ago you investigated the interaction of a system of two masses without any external forces, namely the conservation of momentum of two colliding carts. In this lab you will investigate a similar "collision", but there will be no linear motion, only rotational. Below are some useful equations you may remember from lecture (all scalar). Definition of angular velocity: = v / r Moment of Inertia of a point mass about an axis of rotation r away: I m =mr 2 Moment of Inertia of a circular disc about a perpendicular axis through its center:

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I disk = 1 2 mr 2 Moment of Inertia of a rod about an axis through its center: I rod ,center = 1 12 ml 2 Definition of angular momentum: L =I Kinetic energy of rotation: KE rotational = 1 2 I w 2 Total energy of an object undergoing both translational and rotational motion: KE total = KE translational KE rotational PE translational = 1 2 mv cm 2 1 2 I 2 mgh C.M. Newton's Law in rotational form (tau is the external torque; alpha is the angular acceleration) : =I Equation of motion in rotational form (constant angular acceleration): = 0  t 1 2 t 2 Time-independent version of equation above: 2 = 0 2 2  In addition, the Moment of Inertia of an object of known I 0 , when taken about another axis parallel to the axis used to calculate the known I (when the two axes are a distance h away) is: I = I 0 mh 2 This is also known as the Parallel Axis Theorem. You will perform two experiments real experiments and one video analysis activity: 1. Gently drop a non-rotating rod (which can either be straight or bent into an approximate circle) onto a circular disc rotating at low angular momentum. The disc is permanently mounted on an angular sensor which will give output angular position and speed to Logger Pro. This is the rotational equivalent of the linear collision you performed with the two Pasco carts on the Pasco track. In this experiment the system (disc + rod) experiences no external torques, just as the two carts experienced no external forces; all interactions are internal.
2. Use a small mass, connected to a pulley with a string, to rotate the circular disc. . Here you are using the same equipment as in (1) above, except that you have re-oriented the setup 90 degrees. This is the rotational equivalent of a force causing a previously stationary mass to accelerate linearly. In this experiment there

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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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rot - Rotational Dynamics Objective To investigate the...

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