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Question Number 23059 by Physics lover last updated on 25/Oct/17

Commented by Physics lover last updated on 25/Oct/17

In the arrangement shown here   friction between the spool   (of mass m, moment of inertia I )  and the plank (of mass M)  is sufficient to prevent slipping.  There is no friction between the  plank and the surface inclined at  angle θ.

$${In}\:{the}\:{arrangement}\:{shown}\:{here}\: \\ $$$${friction}\:{between}\:{the}\:{spool}\: \\ $$$$\left({of}\:{mass}\:{m},\:{moment}\:{of}\:{inertia}\:{I}\:\right) \\ $$$${and}\:{the}\:{plank}\:\left({of}\:{mass}\:{M}\right) \\ $$$${is}\:{sufficient}\:{to}\:{prevent}\:{slipping}. \\ $$$${There}\:{is}\:{no}\:{friction}\:{between}\:{the} \\ $$$${plank}\:{and}\:{the}\:{surface}\:{inclined}\:{at} \\ $$$${angle}\:\theta. \\ $$$$ \\ $$

Commented by Physics lover last updated on 25/Oct/17

Find angular acceleration of the  spool .    answer :       [(((m−M)g∙Sin θ )/((m+M)R^2  + I))]∙ R

$${Find}\:{angular}\:{acceleration}\:{of}\:{the} \\ $$$${spool}\:. \\ $$$$ \\ $$$${answer}\:: \\ $$$$\:\:\:\:\:\left[\frac{\left({m}−{M}\right){g}\centerdot{Sin}\:\theta\:}{\left({m}+{M}\right){R}^{\mathrm{2}} \:+\:{I}}\right]\centerdot\:{R} \\ $$

Commented by Physics lover last updated on 25/Oct/17

Also find accleleration of plank  if     (m/M)  < 1    answer :   descend with acceleration  (((M − m) ∙gR^2 ∙ Sin θ )/((m + M )R^2   + I ))

$${Also}\:{find}\:{accleleration}\:{of}\:{plank} \\ $$$${if}\:\:\:\:\:\frac{{m}}{{M}}\:\:<\:\mathrm{1} \\ $$$$ \\ $$$${answer}\::\: \\ $$$${descend}\:{with}\:{acceleration} \\ $$$$\frac{\left({M}\:−\:{m}\right)\:\centerdot{gR}^{\mathrm{2}} \centerdot\:{Sin}\:\theta\:}{\left({m}\:+\:{M}\:\right){R}^{\mathrm{2}} \:\:+\:{I}\:} \\ $$

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