# PH1004_Experiment_4 - PH1004 Exp 4 Rotational Motion Moment...

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PH1004 Exp 4: Rotational Motion. Moment of Inertia. 1 PH 1004 Laboratory Instructions Experiment 4 Rotational Motion. Moment of Inertia. Introduction Previous experiments dealt with the effect of a force on the linear motion of an object that could be assumed to be a point mass. Real objects, however, are of finite extent (length, width, height). When a force acts on an extended object, the resulting motion is a combination of translation and rotation. In this experiment you will analyze the rotating effects of a force. You will explore the concepts of torque, moment of inertia and angular acceleration and investigate how these quantities relate to each other. In particular, you will determine the moments of inertia for a solid circular disk and a ring. You will also test whether the angular momentum is conserved when a ring is dropped onto a rotating disk. An extended body that is free to rotate about an axis will do so under the application of a torque. The resulting angular acceleration is given by Newton’s Second Law for rotation: α τ r r I = (4-1) where τ r is the net applied torque (including any torque caused by friction), α r is the angular acceleration, and I is the moment of inertia. The moment of inertia of a body depends on distribution of its mass about an axis of rotation. Consequently, the same body can have different moments of inertia depending on where the axis of rotation is chosen. In this experiment you will find the moment of inertia of a disk rotating about an axis which is perpendicular to the disk and passing through its center. Overview Figure 4-1 shows a schematic of the experiment. The disk is mounted on a vertical shaft with a heavy base. A string wrapped around the lowest spool (of radius r ), attached to the same vertical shaft, passes over a pulley, where it is attached to a known
PH1004 Exp 4: Rotational Motion. Moment of Inertia. 2 mass. As the mass is released from rest, it accelerates downward with a linear acceleration a (much smaller than the acceleration due to gravity, g ). The tension in the string provides a torque, which rotates the disk about an axis of rotation passing through the center of the vertical shaft. There is also some torque due to friction that resists the rotation. The equation relating the net torque to the moment of inertia and the resultant angular acceleration of the system is given by α τ τ τ I f net = = . (4-2) Here τ f is the frictional torque, and τ is the torque due to the tension in the string. The directions of the torques and the angular acceleration remain the same throughout the experiment (perpendicular to the disk, directed upward for α r and τ r , and downward for f τ r ). Choosing the positive direction for z-axis upwards, perpendicular to the disk, we may say that Equation 4-2 is written for the z-components of the torques and angular acceleration, which are also the magnitudes of those vectors. Figure 4-1 Since the string wrapped around the spool does not slip, one can relate the angular acceleration, α r and the linear acceleration of the hanging mass, a r