Which equation expresses the velocity of an object in circular motion in terms of radius r and orbital period T?

• A. F = ma
• B. v = 2π r / T
• C. L = m v r
• D. v = sqrt(GM/r)

Answer: (B)

When an object moves in a circle, its velocity is the distance it covers along the circular path per unit time. For a circle of radius r, the distance of one complete orbit is 2πr. If that orbit takes a time T, the speed is v = distance/time = 2πr / T. This shows how the linear speed relates directly to the radius and the orbital period. You can also see the same idea in the form v = ωr, where ω = 2π/T is the angular speed.

Other formulas describe different quantities. F = ma is Newton’s second law, not a velocity. L = mvr is angular momentum, which involves velocity but isn’t the velocity expressed purely in terms of r and T. v = sqrt(GM/r) gives the orbital speed in a gravitational field with central mass M and depends on G and M, not just r and T.