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Physics

Mechanics

Easy

Question

A rod of mass m and length L is released from rest from vertical position as shown. The normal force exerted on the rod by ground as function of as rod falls downward without slip

$\frac{m g}{4} (1 - 3 \sin θ)^{2}$
$\frac{m g}{4} (1 - 3 \cos θ)^{2}$
$\frac{m g}{4} (1 - \sin θ)^{2}$
$\frac{m g}{4} (1 - \cos θ)^{2}$

The correct answer is: $fraction numerator m g over denominator 4 end fraction left parenthesis 1 minus 3 cos invisible function application theta right parenthesis squared$

$table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell 1 half I omega squared equals m g L over 2 left parenthesis 1 minus cos invisible function application theta right parenthesis ∣ end cell row cell not stretchy rightwards double arrow omega squared equals fraction numerator 3 g over denominator L end fraction left parenthesis 1 minus cos invisible function application theta right parenthesis end cell row cell text Normal acceleration end text a subscript n equals L over 2 omega squared equals fraction numerator 3 g over denominator 2 end fraction left parenthesis 1 minus cos invisible function application theta right parenthesis end cell row cell text Tangential acceleration end text a subscript t equals L over 2 alpha equals fraction numerator 3 g sin invisible function application theta over denominator 4 end fraction end cell end table table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell f equals m a subscript x equals m open parentheses a comma cos invisible function application theta minus a subscript n sin invisible function application theta close parentheses end cell row cell equals fraction numerator 3 m g over denominator 2 end fraction sin invisible function application theta open parentheses fraction numerator 3 cos invisible function application theta over denominator 2 end fraction minus 1 close parentheses end cell row cell alpha equals fraction numerator 3 g sin invisible function application theta over denominator 2 L end fraction end cell end table table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell m g minus N equals m a subscript y semicolon space of 1em N equals m g minus m a subscript y end cell row cell N equals m open square brackets g minus open parentheses a subscript i sin invisible function application theta plus a subscript n cos invisible function application theta close parentheses close square brackets equals fraction numerator m g over denominator 4 end fraction left parenthesis 1 minus 3 cos invisible function application theta right parenthesis squared end cell end table$

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