First slide

Angular momentum

Question

If L, m denote the angular momentum and mass of the particle a:rd p is linear momentum, which of the following can represent the kinetic energy of the particle moving in a circle of radius .R ?

Easy

A

$\frac{L^{2}}{2 m}$
B

$\frac{p^{2}}{m}$
C

$\frac{L^{2}}{2 {mR}^{2}}$
D

$\frac{1}{2} {mp}^{2}$

Solution

In terms of linear momentum, the K.E. is given by $K.E. = \frac{p^{2}}{2 m}$
Now we consider the K.E in terms of angular momentum L
$\begin{aligned} L = mvR or V = L / (mR) \\ K.E. = \frac{1}{2} {mv}^{2} \end{aligned}$
$Substituting the value of v from eq. (1) in eq. (2), we get K.E. = \frac{1}{2} m (L / mR)^{2} = \frac{L^{2}}{2 {mR}^{2}}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App