In a bicycle,the radius of the rear wheel is | vedclass

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(C) For a bicycle moving with a constant linear velocity $v$ of its center of mass,the velocity of any point on the rim of the wheel relative to the g

Vedclass · Accepted Answer

$v_F = v_r$

Vedclass · Answer

(C) For a bicycle moving with a constant linear velocity $v$ of its center of mass,the velocity of any point on the rim of the wheel relative to the ground is given by the vector sum of the translational velocity and the rotational velocity.At the topmost point of a wheel,the linear velocity is $v_{top} = v_{translational} + v_{rotational} = v + r\omega$.Since the bicycle is moving as a single rigid body,the translational velocity $v$ of the center of mass for both wheels is the same.For pure rolling motion,$v = r\omega$,so $v_{top} = v + v = 2v$.Since both wheels move forward with the same translational speed $v$ of the bicycle,the speed of the topmost point for both the front wheel $(v_F)$ and the rear wheel $(v_r)$ is $2v$.Therefore,$v_F = 2v$ and $v_r = 2v$,which implies $v_F = v_r$.

In a bicycle,the radius of the rear wheel is twice the radius of the front wheel. If $r_F$ and $r_r$ are the radii,and $v_F$ and $v_r$ are the speeds of the topmost points of the wheels respectively,then:

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