Question

A flat surface of a thin uniform disk $A$ of radius $R$ is glued to a horizontal table. Another thin uniform disk $B$ of mass $M$ and with the same radius $R$ rolls without slipping on the circumference of $A$, as shown in the figure. A flat surface of $B$ also lies on the plane of the table. The center of mass of $B$ has fixed angular speed $\omega$ about the vertical axis passing through the center of $A$. The angular momentum of $B$ is $nM\omega R^2$ with respect to the center of $A$. Which of the following is the value of $n$ ?

• A. 2
• B. 5
• C. $\frac{7}{2}$
• D. $\frac{9}{2}$

Answer 1

Answer: (B)

$v=\omega (2R)$
$v={\omega }_{0}R:$ no slipping
$\therefore {\omega }_0=2\omega$

$\overrightarrow{L}=m\overrightarrow{r}\times {\overrightarrow{v}}_c+I_c{\omega }_0$
$=M2Rv+\frac{1}{2}M{R}^2{\omega }_0$
$=4M{R}^2\omega +\frac{1}{2}M{R}^2(2\omega )=5M{R}^2\omega$
$\therefore n=5$