First slide

General Planar motion

Question

A disc of mass M and radius R rolls without slipping on a horizontal surface. If the velocity of its center is v₀, then the total angular momentum of the disc about a fixed point P at a height (3/2)R above the center C

Easy

A

increases continuously as the disc moves away
B

decreases continuously as the disc moves away
C

$is equal to 2 M R v_{0}$
D

$is equal to M R v_{0}$

Solution

$\begin{array}{l} \vec{L} = I_{CM} \vec{ω} + m \vec{r} \times {\vec{v}}_{CM} \\ = \frac{M R^{2}}{2} ω (- \hat{k}) + M \frac{3}{2} R (- \hat{j}) \times v_{0} \hat{i} = M R v_{0} \hat{k} \end{array}$

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