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the radus if the rear wheel of bicycle i...

the radus if the rear wheel of bicycle is twice that of the front wheel. When the bicycle is moving . The angular speed of the rear wheel compared to that of the front is

A

Greater

B

smaller

C

same

D

exact double

Text Solution

Verified by Experts

The correct Answer is:
B
As no external torque acts on the system, angular momentum will remain conserved.l According to law of conservation of angular momentum, Acorrding to law of conservation of angular momentum , `I_(1)Omega_(1) = I_(2)Omega_(2)`
` or m_(r)r_(r)^(2) Omega_(r) = m_(f) r_(f)^(2) Omega_(f)`
Where the subscripts r and f denote the rear and front.
` m(2r_(f))^(2) Omegar = mr_(f)^(2) Omega_(f) [r_(r) = 2r_(f) ` (Given)]
` therefore 4Omega_(r) = Omega_(f) or Omega_(r) = (Omega_(f))/4 `
Hence, the angular velocity of rear wheel will be smaller compared to frot wheel.
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