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Net Acceleration for Non Uniform Circular Motion

two loops P a...

Question

two loops P and Q are made from a uniform wire. The radii of P and Q are R1 and R2 respectively and their moment of inertia about axes normally through center are I1 and I2 respectively. If I2/I1 = 4 then find R2/R1

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Solution

$\frac{I_{1}}{I_{2}} = \frac{1}{4} \frac{m_{1} {r_{1}}^{2}}{m_{2} {r_{2}}^{2}} = \frac{1}{4} L e t m a s s p e r u n i t l e n g t h o f b o t h w i r e s b e s a m e = q a s s u m i n g t h a t b o t h w i r e s a r e m a d e f r o m s a m e m a t e r i a l \frac{q 2 π {r_{1}}^{3}}{q 2 π {r_{2}}^{3}} = \frac{1}{4} \frac{q 2 π {r_{1}}^{3}}{q 2 π {r_{2}}^{3}} = \frac{1}{4} t h e n \frac{r_{1}}{r_{2}} = \sqrt[3]{\frac{1}{4}} I f y o u a s s u m e t h a t m a s s o f b o t h r i n g s a r e s a m e t h e n, \frac{m_{1} {r_{1}}^{2}}{m_{2} {r_{2}}^{2}} = \frac{1}{4} \frac{{r_{1}}^{2}}{{r_{2}}^{2}} = \frac{1}{4} \frac{r_{1}}{r_{2}} = \frac{1}{2} r e g a r d s$

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Net Acceleration for Non Uniform Circular Motion

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