Question

A uniform solid cylinder is given a linear velocity and angular velocity, so that it rolls without sliding up the incline. Out of the four points A,B,C and centre of mass, about which point its angular momentum will be conserved ?

(A and C are taken at appropriate distance)

• A. Point A
• B. Point B
• C. Point C
• D. Centre of mass

Answer 1

The correct option is C Point C

Whether the cylinder rolls up or rolls down, the static friction will always act up the incline and its value will be $f_r=\frac{mg\sin \theta }{1+\frac{I}{m{R}^2}}$, which is less than $mg\sin \theta$.
So about point C which is above CM, torque can be balanced.
And about point C , its angular momentum will be conserved.
We can also find the distance of point C from CM. Let it be $x$. Applying torque balance about point C:
$\left(mg\sin \theta \right)\left(x\right)$ = $\left(\frac{mg\sin \theta }{1+\left(\frac{1}{2}\right)}\right)(R+x)$
Solving we get $x=2R$