Question

${\boxed{\underline{\red{QUESTION : }}}}$
A homogeneous disc of weight W and radius R rotates about the vertical axis OZ, the initial angular velocity being omega_(0). During the motion, the brake block A is pressed to the disc,with a radial force N for t_(0) seconds and the disc comes to rest because of friction. Find the coefficient of friction.​

Answer 1

☆QUESTION ☆

A homogeneous disc of weight W and radius R rotates about the vertical axis OZ, the initial angular velocity being omega_(0). During the motion, the brake block A is pressed to the disc,with a radial force N for t_(0) seconds and the disc comes to rest because of friction. Find the coefficient of friction.

☆ANSWER ☆

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Answer 2

$\huge{\underline{\underline{\sf{\blue{SOLUTION:-}}}}}$

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$\sf{\underline{\pink{Answer-}}}$

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• $\sf the \: coefficent \: of \: friction \: is \: M_O = \frac{WW_O}{2gt_ON}$

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$\sf{\underline{\pink{Given-}}}$

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• A homogeneous disc of weight W and radius R rotates about the vertical axis OZ

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• the initial angular velocity being⠀⠀ omeg$a_(0)$

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• During the motion, the brake block A is pressed to the disc,with a radial force N for $t_(0)$

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• seconds and the disc comes to rest because of friction.

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$\sf{\underline{\pink{Find-}}} </h2><h2>$

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• the coefficient of friction.

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$\sf{\underline{\pink{Explanation-}}} </h2><h2>$

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$\sf\longrightarrow F = NM_O$

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$\sf\longrightarrow F \: due\: to \: the \: friction = M_O NR$

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$</p><p>\sf\longrightarrow O = W_O + \alpha + t_O$

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$\sf\longrightarrow \alpha = \frac{W_O}{t_O}$

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$\sf{\underline{\pink{Putting\:the\:values:-}}}$

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$\sf\longrightarrow F = I \: \: \alpha = M_ONR$

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$\sf\longrightarrow \frac{ {MR }^{2} }{2}\frac{(W_O}{t_O}= M_ONR$

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$\sf\longrightarrow W = mg$

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$\sf{\underline{\blue{Now-}}}$

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• $\sf Hence,\: the \: coefficent \: of \: friction \: is \: M_O = \frac{WW_O}{2gt_ON}$

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