Moment of Inertia Objectives • To investigate the different moment of inertia for different shapes Materials/Resources •

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Moment Of Inertia Objectives To Investigate The Different Moment Of Inertia For Different Shapes Materials Resources 1 (51.47 KiB) Viewed 33 times

Can you Explain any physical assumptions made, the relevant principle, and how the measured and calculated values relate ?
The measured values is mass, radius, and speed

Moment Of Inertia Objectives To Investigate The Different Moment Of Inertia For Different Shapes Materials Resources 2 (34.15 KiB) Viewed 33 times

Moment Of Inertia Objectives To Investigate The Different Moment Of Inertia For Different Shapes Materials Resources 3 (21.37 KiB) Viewed 33 times

Moment of Inertia Objectives • To investigate the different moment of inertia for different shapes Materials/Resources • Pasco 550 interface box and Computer with Capstone software • Rotational platform, Ring, Disk, Allen wrench • Super pulley with mounting rod and Photogate • Slotted mass set and Hangar • String and Scissors • Bubble level • Balance and Mass set • Meter stick and Calipers • Scientific calculator Introduction Rotational inertia (or moment of inertia) tells us how the mass of a rotating body is distributed about its axis of rotation. For a single point mass treated as a rotating body (imagine a point mass of mass m tied to a fixed point by a massless rod of length R), the rotational inertia, I, is mR2. Consequently, rotational inertia has the SI units of kg.m2. If there are many of these point masses on massless rods rotating about a common axis, the rotational inertia of that system is given by (mR2), or the sum of the rotational inertia associated with each mass. If enough masses are tightly packed around the same axis, it is easy to see how that a ring is formed, whose mass, M, is the sum of the masses that comprise it, Em. The rotational inertia of this ring is given by tring = MR2 Note that this equation assumes that the ring has nothickness. For a ring that is too thick for that assumption to be accurate, a better equation to use is given by 1
lving stier M(R} + R) where M is the mass of the ring. R; in the inner radius of the ring, and R, is the outer radius of the ring as shown in Figure 9-1. Ping PAESCO) Similarly, the rotational inertia of a solid disk rotating about its center (See Figure 9-2) is given by where M is the mass of the disk, and R is the radius of the disk. What this means is that a disk of mass M is half as hard to rotate about its axis as a ring of the same mass would be. This is because the farther a mass is from its axis of rotation the farther it must travel to rotate through the same angle as a mass that is closer to the axis, and more of the mass is closer to the axis for a disk than for a ring with the same mass. In this experiment, we will also measure the rotational inertia of a disk about its diameter (See Figure 9-3) which is given by laiskortcut MR Fie od 1. Dial rating atent contre rand Dune Care of PASCO ) In order to find the rotational inertia experimentally, a known torque, t, is applied to the object, and the resulting angular acceleration, a, is measured. Since r = la. where the angular acceleration, a, is equal to air (r is the radius of the cylinder about which the thread is wound.) and is the torque caused by the weight hanging from the thread which is
wrapped around the base of the apparatus as shown in Figure 4. The torque on the apparatus is given by T=YT where is the tension in the thread when the apparatus is rotating Applying Newton's Second Law for the hanging mass, m, gives EF = mg - Tema Solving for the tension in the thread gives T= m(g-a) Once the linear acceleration of the mass (w) is determined, the torque and the angular acceleration can be obtained for the calculation of the rotational inertia. rotational disk 1. "A" base hanging mass mg Figure Be Rotutional Apparatus and Free Bali Durant Course of PASCO elenfic) 3