You are pedaling a bicycle at 9.8 m/s. the radius of the wheels of the bicycle is 51.9cm. the angular velocity of rotation of the wheels is

There is a relationship between rotational motion and rectilinear motion. These are all derived from the basic laws of motions - that is Newton's Laws of Motion. The value of 9.8 m/s is the linear velocity. To convert it to angular velocity, the equation is

v=rω, where
v is the linear velocity in m/s
r is the radius of the wheels in m
ω is the angular velocity in rad/s

If r is in 51.9 cm, that is equivalent to 0.519 m. We make sure to be consistent of the units because we are going to use velocity in m/s later on.

v=rω
ω = v/r = 9.8 m/s ÷ 0.519 m
ω = 18.88 rad/s

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