Question

A cylinder is rotating with angular velocity ω and angular acceleration α at any instant, while translating with velocity V. Find the net acceleration of point P at this instant (radius of cylinder is R).

• A. $\alpha R$
• B. $\left(\sqrt{{\alpha }^2+\frac{v^4}{R^4}}\right)R$
• C. $\left(\sqrt{{\alpha }^2+{\omega }^4}\right)R$
• D. Both (b) and (c)

Answer 1

The correct option is C

$\left(\sqrt{{\alpha }^2+{\omega }^4}\right)R$

The tangential acceleration due to angular acceleration $\alpha =\alpha R$

The normal (centripetal acceleration) = ${\omega }^{2}R$

$\therefore$ Net acceleration

$=\sqrt{{\alpha }^2{R}^2+{\omega }^4{R}^2}$

$=\left(\sqrt{{\alpha }^2+{\omega }^4}\right)R$

[Note that velocity v of the centre of mass has no effect on the acceleration of P, this is because it is a constant]