Question Number 23059 by Physics lover last updated on 25/Oct/17
Commented by Physics lover last updated on 25/Oct/17
$${In}\:{the}\:{arrangement}\:{shown}\:{here}\: \\ $$$${friction}\:{between}\:{the}\:{spool}\: \\ $$$$\left({of}\:{mass}\:{m},\:{moment}\:{of}\:{inertia}\:{I}\:\right) \\ $$$${and}\:{the}\:{plank}\:\left({of}\:{mass}\:{M}\right) \\ $$$${is}\:{sufficient}\:{to}\:{prevent}\:{slipping}. \\ $$$${There}\:{is}\:{no}\:{friction}\:{between}\:{the} \\ $$$${plank}\:{and}\:{the}\:{surface}\:{inclined}\:{at} \\ $$$${angle}\:\theta. \\ $$$$ \\ $$
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](https://www.tinkutara.com/question/Q23064.png)
$${Find}\:{angular}\:{acceleration}\:{of}\:{the} \\ $$$${spool}\:. \\ $$$$ \\ $$$${answer}\:: \\ $$$$\:\:\:\:\:\left[\frac{\left({m}−{M}\right){g}\centerdot{Sin}\:\theta\:}{\left({m}+{M}\right){R}^{\mathrm{2}} \:+\:{I}}\right]\centerdot\:{R} \\ $$
Commented by Physics lover last updated on 25/Oct/17
$${Also}\:{find}\:{accleleration}\:{of}\:{plank} \\ $$$${if}\:\:\:\:\:\frac{{m}}{{M}}\:\:<\:\mathrm{1} \\ $$$$ \\ $$$${answer}\::\: \\ $$$${descend}\:{with}\:{acceleration} \\ $$$$\frac{\left({M}\:−\:{m}\right)\:\centerdot{gR}^{\mathrm{2}} \centerdot\:{Sin}\:\theta\:}{\left({m}\:+\:{M}\:\right){R}^{\mathrm{2}} \:\:+\:{I}\:} \\ $$