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Standard XII

Physics

Relation between Linear and Angular Speed

A solid spher...

Question

A solid sphere of mass m and radius $R$ is rolling without slipping as shown in figure. Find angular momentum of the sphere about z-axis.

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Solution

$L = m v r_{⊥} + I_{c} ω$
$= m v R + (\frac{2}{5} m R^{2}) (\frac{v}{R})$
$= \frac{7}{5} m v R$
This is clockwise. or along negative z-axis.
$∴ \to L = (- \frac{7}{5} m v R)^k$

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A solid sphere of mass m and radius R is rolling without slipping as shown in figure. Find angular momentum of the sphere about z-axis.

L=mvr⊥+Icω=mvR+(25mR2)(vR)=75mvRThis is clockwise. or along negative z-axis.∴→L=(−75mvR)^k

A solid sphere of mass m and radius $R$ is rolling without slipping as shown in figure. Find angular momentum of the sphere about z-axis.

$L = m v r_{⊥} + I_{c} ω$
$= m v R + (\frac{2}{5} m R^{2}) (\frac{v}{R})$
$= \frac{7}{5} m v R$
This is clockwise. or along negative z-axis.
$∴ \to L = (- \frac{7}{5} m v R)^k$