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You have a grindstone that is 90.0kg, has a radius of 0.34m and is turning st 90 rpm. You press a steel axe against it with a radial force of 20.0N. Assuming that the kinetic coefficient of friction between steel and stone is 0.2, (a) calculate the angular acceleration of the grindstone (b) calculate the turns made by stone before it came to a stop

I can’t find the mistake in my working. My answer for (a) is half what it should be which in turn affected my answer for (b) by making it twice what it should be. enter image description here

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  • $\begingroup$ Answers are 0.26rad/s^2 and 27 revs for reference. $\endgroup$
    – Gonzales
    Commented Aug 18, 2021 at 3:10
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    $\begingroup$ To supplement Al Brown's answer, the reason why you cant use $F=ma$ is this equation accounts for the acceleration of the center of mass of the system, in which $a=0$ in this question. So you need to use the torque equation. $\endgroup$
    – Kksen
    Commented Aug 18, 2021 at 3:57
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    $\begingroup$ That actually makes so much sense. Thank you! $\endgroup$
    – Gonzales
    Commented Aug 18, 2021 at 4:25
  • $\begingroup$ Hello! Please read How do I ask homework questions on Physics Stack Exchange? and edit your question accordingly. Also, it is preferable to type out screenshots or images of text; for formulae, one can use MathJax. Thanks! $\endgroup$
    – jng224
    Commented Aug 18, 2021 at 15:14

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You cannot use $F=ma$ when working with angular acceleration. You have to use $\tau=I \alpha$. $\text{ } \tau$ is torque, tangent-force times radius. Alpha, $\alpha$, is angular acceleration, $\frac{d \omega}{dt}$. $\text{ } I$ is moment of inertia. Look for the formula for the $I$ of a disc.

That’s all the help allowed to give.

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    $\begingroup$ Ah that explains it. I kinda skipped the chapter on rotational inertia. Thank you so much! $\endgroup$
    – Gonzales
    Commented Aug 18, 2021 at 3:53
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    $\begingroup$ Other common concept is that angular momentum is $I\omega$. (Like $mv$ is for linear) $\endgroup$
    – Al Brown
    Commented Aug 18, 2021 at 3:56

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