# 47 - Rotational mechanics Questions Answers

**Asked By: AMAN KUMAR**

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**Joshi sir comment**

No horizontal force.

Draw a perpendicular from centre to horizontal plane. Then calculate horizontal distance.

Now solve.

If any problem, then inform

**Asked By: AVRANIL SAHA**

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**Joshi sir comment**

$InfirstcaseF=2T=150\phantom{\rule{0ex}{0ex}}soT=75newton,\phantom{\rule{0ex}{0ex}}Nowinsecondcasesystemisfreetomove\phantom{\rule{0ex}{0ex}}accelerationofthesystema=F/20\phantom{\rule{0ex}{0ex}}for10kgrodF-2T=10a=10(F/20)=F/2\phantom{\rule{0ex}{0ex}}\Rightarrow F-(F/2)=2T\Rightarrow F=4T=300newton$

what is the moment of inertia of a cube about its diagonal?

**Asked By: SHIV GOVIND**

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**Joshi sir comment**

$Momentofinertiaofacubeaboutalineperpendicularto\phantom{\rule{0ex}{0ex}}itsonefaceandpas\mathrm{sin}gthroughitscentreism{a}^{2}/6\phantom{\rule{0ex}{0ex}}soaboutdiagonalinertia={l}^{2}{I}_{x}+{m}^{2}{I}_{y}+{n}^{2}{I}_{z}\phantom{\rule{0ex}{0ex}}=({l}^{2}+{m}^{2}+{n}^{2}){I}_{x}(here{I}_{x}={I}_{y}={I}_{z})\phantom{\rule{0ex}{0ex}}={I}_{x}=m{a}^{2}/6\phantom{\rule{0ex}{0ex}}l,m,naredirection\mathrm{cos}inesofthreelinespas\mathrm{sin}gthrouge\phantom{\rule{0ex}{0ex}}centreofcubeandperpendiculartoeachother$

A rotating ball hits a rough horizontal plane with a vertical velocity and angular velocity . Given that the coefficient of friction is and the vertical component of the velocity after the collision is , find:

a) the angular velocity after collision;

b) the impulsive ground reaction during the collision

**Asked By: UDDESH KUMAR SABAT**

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**Joshi sir comment**

on applying momentum impulse theorem along vertical

-mv+Ndt = mv/2 (1)

by angular momentum angular impulse theorem

$2m\omega {r}^{2}/5-\mu Ndtr=2m{\omega}^{,}{r}^{2}/5\left(2\right)$By eq. (2) get angular velocity.

impulsive ground reaction = $\sqrt{{\left(Ndt\right)}^{2}+{\left(\mu Ndt\right)}^{2}}$by using eq. (1), solve it

**What is the minimum coefficient of friction for a solid sphere to roll without slipping on an inclined plane of inclination θ?**

**Asked By: SWATI KAPOOR**

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**Joshi sir comment**

friction f = mgsinθ/[1+(mr^{2}/I)]

solve for sphere and compare to μmgcosθ