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$\cdot$ When the power is turned off on a turntable spinning at 78.0 rpm, you find that it takes 10.5 revolutions for it to stop while slowing down at a uniform rate. (a) What is the angular acceleration (in rad $s^{2} )$ of this turntable? (b) How long does it take to stop after the power is turned off?

a) $-0.5058 \mathrm{rad} / \mathrm{s}^{2}$b) 16.2$s$

Physics 101 Mechanics

Chapter 9

Rotational Motion

Physics Basics

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Cornell University

Simon Fraser University

Hope College

University of Winnipeg

Lectures

04:16

In mathematics, a proof is…

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In mathematics, algebra is…

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$\cdot$ A turntable that s…

02:01

A phonograph turntable rot…

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A turntable reaches an ang…

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let's start off by writing our knowns in this problem. So we know that the final your velocity is going to be zero radiance per second. We know the initial angular velocity is eagle to 78 revolutions per minute. Well, we needed commercials and Iranians for second, and so I'm gonna have minutes in the top seconds in the denominator. One minute, 60 seconds. And so the minutes here cancels with the permits here and then I've revolution with the new mayor, so I'm going to put them in the denominator. And then I welcome Earth element Iranians. One revolution is to fire radiance. Doing the sound gives an initial and your velocity of 8.17 radiance per second. And then we're also told that the angle throughout this process is 10.5 revolutions. We need to cover this in Iranians. So we have this conversion factor. One revolution is to buy radiance. This gives 65.97 radiance. And now that everything is in the proper units, we can use a rotational cinematic equation to solve for the angular acceleration. The one I'm going to use is Omega Squared is equal to Omega not squared. Plus two Alfa. They don't mind state or not. And then I plug in zero. Here Omega not is 8.17 plus two Alfa. And then I have 65 for 97 here. Solving this for Alfa gives us negative zero plane negative 0.5 06 Radiance percent square. It's negative because the tape the turntable slowing down now Prince of its angular velocity is decreasing. So the extortions name in part B. We want to figure out the time this takes. And so the kingdom attic equation I'm going to use now It's Oh, my God is equal to Omega, Not LaSalle. Fatih, We just found Alfa and we've no no Megan Omega. Not since the beginning. And so you can just easily sell for tea in this. And when we do that, we get 16.15 seconds. NASA final answer

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