Moment of Innertia

xlsx

School

CUNY College of Staten Island *

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Course

PHY-116

Subject

Mechanical Engineering

Date

Jan 9, 2024

Type

xlsx

Pages

Uploaded by youstena2004

Your name Youstina Khalil Lab Partner Mutlu Erkin Date 11/10/2023 List of equipment Linear track motion sensor objects logger pro Table1: Calculating coeficient of rotational inertia for different objects by rolling Incline angle in degrees 6.9 Object Theoretical Experimental PE b value Solid Sphere 0.40 0.8422 0.824 0.430 7.48 0.8642 0.7662 Solid Cylinder 0.50 0.7364 0.796 0.481 3.87 0.8425 0.8090 0.67 0.7705 0.725 0.626 6.05 0.7028 0.7007 1.00 0.5816 0.562 1.097 9.73 0.5475 0.5567 Figure 1 Experiment setup Following functions for solid sphere only, you can do the rest by using this Average accelaration=AVERAGE(E23:E25) b(calculated) =(9.81*SIN(RADIANS(G$20))/F23)-1 PE=ABS(D23-G23)/D23*100 Questions: Discussion and conclusion Experimental acceleration [ ] Experimental average acceleration [ ] b(calculated) b=( g sin /a)-1 θ Hollow Sphere Hollow Cylinder 1. What is the moment of inertia means, how that affect to the motion? 2. If you are dropping a solid ball which include both rotational and translational motions, how do you solve this problem. Explain, what will happen to the final velocity if there is a rotational motion. 3. If you roll solid and hollow spheres on the incline at the same time, which one reach ground first? Why? 4. If you spin on the tunable table, you can move your arms close together to your body, then you will spin faster, why? The moment of inertia represents an object's resistance to rotational motion around a specific axis, impacting how quickly or slowly the object can respond to a rotational force. When dropping a solid ball, the final velocity is determined by considering both translational and rotational kinetic energy contributions, with the rotational motion leading to a slightly reduced final velocity. Both solid and hollow spheres, having the same mass and radius and neglecting external factors, will reach the ground simultaneously when rolled down an incline due to equal acceleration under gravity, as per Galileo's principle of equal acceleration for all objects in a vacuum. Bringing your arms closer to your body while spinning on a turntable decreases your rotational inertia, leading to an increase in angular velocity due to the conservation of angular momentum, similar to the effect observed when figure skaters pull their arms closer during a spin. The Data Tables Moment of Inertia lab systematically investigated the intricate interplay between moment of inertia, mass distribution, and shape. By measuring the deceleration time of a turntable with varied mass configurations, the data illuminated distinct trends: configurations with mass concentrated near the axis exhibited faster deceleration, highlighting the direct influence of mass distribution on rotational motion. These findings underscore the nuanced relationship between moment of inertia and rotational dynamics, crucial for applications in engineering and physics where precise control over rotational motion is paramount.

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