PHYS161_MomentOfInertia_Spring_2106 - Physics 161 Moment of...

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Physics161Moment of Inertia IntroductionIn this experiment we will study the effect of a constant torque on a symmetrical body. In Part I you will determine the angular acceleration of a diskwhen a constant torque is applied to the disk. From this we will measure its moment of inertia, which we will compare with a theoretical value. In Part II, you will observe the relationship between torque, moment of inertia and angular acceleration for a rotating rod with two masses on either end. You will vary the mass connected (and therefore the torque applied) to the rod by two pulleys. You will also change the moment of inertia of the rod system by changing the distance of the masses from the center of mass of the rod. ReferenceYoung and Freedman, University Physics, 13th Edition: Chapter 3, section 4; Chapter 9, sections1-4TheoryMoment of inertia is a measure of the distribution of mass in a body and how difficult that body is to accelerate angularly. For both parts of the experiment, a falling mass will accelerate a rotating object in the horizontal plane. In Part I, the object will be a disk. In Part II, you will find the moment of inertia of a rod with two masses attached to it.The basic equation for rotational motion is:I(1)where is angular accelerationin units of rad/s2, is applied torquein N m, and finally the moment of inertia or rotational inertiain units of kg m2. For a uniform disk pivoted about the center of mass, the theoretical moment of inertia is221MRIdisk(2)where M is the mass of the disk and R is the radius of the disk. In Part I we measure the angular acceleration,α, and use this to calculate moment of inertia, I, which we will compare with the theoretical value of I
Iis
.
In Part IIthe moment of inertia is the sum of the moments of inertia of the two masses and the rod. For the masses that slip onto the rod, we will assume point masses. Thus, the moment of inertia for one of the two masses is:2mrImass(3)where ris the distance of the center of massfrom the axis of rotation located at the center of the rod. Because the masses can be moved along the rod, rwill be adjusted to change their moment of inertia. The moment of the inertia of the rod with mass Mand a length Lis: 2121LMIrodrod(4)The moment of inertia for a rod with length Land two masses on each end at a distance rsimply the sum of the components as defined by Equations 3 and 4:212122LMmrIrod(5)
is

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