First slide

Rolling motion

Question

A uniform solid disc is rolling on a horizontal surface. At a certain instant B is the point of contact and A is at height 2R from ground, where R is radius of disc:

Moderate

A

The magnitude of the angular momentum of the disc about B is thrice that about A.
B

The angular momentum of the disc about A is anticlockwise.
C

The angular momentum of the disc about B is clockwise
D

The angular momentum of the disc about A is equal to that about B.

Solution

$\vec{L} = \vec{r} \times M {\vec{V}}_{cm} + I_{cm} ω$
$\begin{array}{l} L_{B} = mvR + \frac{1}{2} {mR}^{2} ω (v = rω) \\ L_{B} = \frac{3}{2} mv R \\ L_{A} = - mvR + \frac{1}{2} {mR}^{2} ω \Rightarrow \frac{1}{2} mvR \\ ∴ |L_{B}| = 3 |L_{A}^{'}| \end{array}$
$\begin{array}{l} As L_{A} = - ve i.e., in (ACW) direction \\ L_{B} = + ve i.e., in (CW) direction \end{array}$

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