In the figure below, the disk will have a rotational inertia lexp. The string connecting the rotating object via the pulley to the hangingmass pulls at a distance roxle from the axis of rotation. (This radius is the spindle radius in the video.)Top View of Axlerotational diskaxleaxle"A" basehangingmassstringIexpa , derive the following expression for lexp using the hanging mass, mh, the measuredUsing the equation for torque, T =acceleration of the hanging mass, a, the acceleration due to gravity, g, and raxle-lexp = m,raxte - 1)The equation above contains the acceleration of the hanging mass, but this is not measured directly. What is the linear acceleration ofthe hanging mass if it starts from rest and falls a distance h in a time t? Plug your answer into the equation for lexn above.what do uv eed to do? nal The procerr of hal tuW need tu do ? chau Theprocens of naa tUgiven er Iexp. The veplace "a" ingetequattantenms t distance "n" and tme 4".

Given that: Rotational inertia of disk=IexpRadius of disk=raxleHanging mass=mhDistance travelled by the hanging mass=hTime taken=tFrom FBD:mhg-T=mhaT=mhg-mhaAgain:Torque=IexpαHere, Torque=TraxleFor pure rolling,α=araxle Hence,Traxle=Iexparaxle(mhg-mha)raxle=Iexparaxle(mhg-mha)r2axle=Iexpamha(ga-1)r2axle=IexpaIexp=mhr2axle(ga-1)Now from kinematic equation:h=ut+12at2a=2ht2 [as initial velocity is zero]Thus:Iexp=mhr2axle(ga-1)if we plug in the value of a,Iexp=mhr2axle(g2ht2-1)Iexp=mhr2axle(gt22h-1)

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Physics

In the figure below, the disk will have a rotational inertia lexp. The string connecting the rotating object via the pulley to the hanging mass pulls at a distance roxde from the axis of rotation. (This radius is the spindle radius in the video.)

In the figure below, the disk will have a rotational inertia lexp. The string connecting the rotating object via the pulley to the hanging mass pulls at a distance roxde from the axis of rotation. (This radius is the spindle radius in the video.)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Torque

Torque is the rotational equivalent of linear force in physics and mechanics. Based on the course of study, it is also known as the moment of force, rotational force, or turning effect.

Question

In the figure below, the disk will have a rotational inertia lexp. The string connecting the rotating object via the pulley to the hanging
mass pulls at a distance roxle from the axis of rotation. (This radius is the spindle radius in the video.)
Top View of Axle
rotational disk
axle
axle
"A" base
hanging
mass
string
Iexpa , derive the following expression for lexp using the hanging mass, mh, the measured
Using the equation for torque, T =
acceleration of the hanging mass, a, the acceleration due to gravity, g, and raxle-
lexp = m,raxte - 1)
The equation above contains the acceleration of the hanging mass, but this is not measured directly. What is the linear acceleration of
the hanging mass if it starts from rest and falls a distance h in a time t? Plug your answer into the equation for lexn above.
what do uv eed to do? nal The procerr of hal tu
W need tu do ? chau The
procens of naa tU
given er Iexp. The veplace "a" in
get
equattan
tenms t distance "n" and tme 4".

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