# Lab5 - Rotational Dynamics Rahel Gunaratne PHYS 1001 A3 TA...

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Rotational DynamicsRahel GunaratnePHYS 1001 A3TA: N.M. Partner: James GrecoStation: 7101067324Data Performed: 11/09/2017Date Submitted: 11/15/2017
1.)Purpose: To determine the rotational inertia of an object, as well as study the conservation of angularmomentum. 2.)Theory: Based on Newton’s second law, the rotation of a rigid object accelerating under a force τ;torque can be characterized by:=τ ;τ=dLdt(1)Where αis the angular acceleration and Lis the angular momentum defined by:L=Iω.(2)Where Iis the rotational inertia of an object and ωis the angular velocity.In the experiment, a weight is dropped to induce a torque. The forces acting along the vertical axis ischaracterized by the following equation: M a=M gT(3)Whereais the final acceleration. Tis the tension caused by the rotational inertia of the object, andcan be characterized by torque τas follows:τ=R×T(4)Where R is the distance from the axis of rotation to the string and combining it with equation (1):=R×T(5)When the angle is 90 degrees, it is reduced to:=RT(6)As a=α R,and combining equations (3) and (6), the angular acceleration can be defined as:α=MgRI+M R2(7)Rearranging to isolate for I:1
I=MgRαM R2(8)Equation (8) allows the rotational inertia of the object to be calculated knowing the mass of the weight M,the angular acceleration α, and the distance from the axis of rotation to the string R. This equation isused by LoggerPro to calculated rotational inertia using measured values. The rotational inertia of a rod can be calculated using the equation:Irod=MrodL212(9)Where M is the mass of the rod, and L is the length of the rod. Similarly, for a disk:Idisk=MdiskR22(10)For the final test, Disk 2 is lowered onto a spinning Disk 1, with a known angular momentum, and thefinal momentum is measured. Figure 1. A diagram of lowering the disk at rest onto the rotating disk1Assuming that the friction between the 3-step pulley and the axis is very small, the initial angular momentum can be stated as:Linitial=I1ωo(11)Where I1is the rotational inertia of the first rotating disk, then the final angular momentum is:2
I(¿¿1+I2)ωfLfinal=¿(12)Where I2
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