Tuesday, 18 October 2016

newtonian mechanics - Why acceleration comes to be diffrent when using $F=ma$ and when using $tau = I alpha $?



Consider a Disc of mass $M$ and radius $R$, I applied force $F$ tangentially on it. Now using $F=Ma$ , acceleration comes up to $$a=F/M$$


Now, let's use the torque equation: Here, the moment of inertia $I$ is $\frac12MR^2$ , and let $\alpha$ be the angular acceleration. Now, torque equals $FR$, so $$FR=\frac12MR^2\alpha$$ and, putting the rolling without slipping assumption $a=\alpha R$, we get $$a=2F/M$$ What gives rise to this discrepancy?




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