A wheel is rolling on the ground with a speed | vedclass

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(A) For a wheel rolling without slipping,the velocity of the center of mass is $v = 2 \ m/s$. At any point on the rim,the velocity is the vector sum o

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$2\sqrt{2} \ m/s$

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(A) For a wheel rolling without slipping,the velocity of the center of mass is $v = 2 \ m/s$. At any point on the rim,the velocity is the vector sum of the translational velocity $(v)$ and the rotational velocity $(v = r\omega)$. For a wheel rolling with speed $v$,the magnitude of the rotational velocity at the rim is also $v$. At the endpoints of the horizontal diameter,the translational velocity vector is horizontal ($v$ to the right),and the rotational velocity vector is vertical ($v$ upwards or downwards). Since these two vectors are perpendicular,the resultant velocity $v_{res}$ is given by: $v_{res} = \sqrt{v^2 + v^2} = \sqrt{2v^2} = v\sqrt{2}$. Substituting $v = 2 \ m/s$: $v_{res} = 2\sqrt{2} \ m/s$.

$A$ wheel is rolling on the ground with a speed of $2 \ m/s$. What is the velocity of the endpoints of the horizontal diameter of the wheel?

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