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6.System of Particles and Rotational Motion
normal
$A$ time varying force $F = 2t$ is applied on a spool rolling as shown in figure. The angular momentum of the spool at time $t$ about bottommost point is:
A
$\frac{{{r^2}{t^2}}}{R}$
B
$\frac{{{{(R + r)}^2}}}{r}\, t^2$
C
$(R + r)t^2$
D
data is insufficient
Solution
Change in angular momentum(L) = Torque $\frac{d L}{d t}=\tau$
$\Rightarrow d L=\tau d t$
Taking torque about lowest point distance of force applied from lowest point $=(R+$$r)$
$\tau=2 t(R+r)$$…(1)$
$\Rightarrow d L=2 t(R+r) d t$
at after time t, the angular momentum becomes
$L=\int_{0}^{L} d L=\int_{0}^{t} 2 t(R+r)$
$\Rightarrow L=(R+r) t^{2}$
Standard 11
Physics
