From the relation v = 2π r / T, what is T expressed as in terms of radius r and speed v?

• A. T = v / (2π r)
• B. T = 2π r / v
• C. T = r / v
• D. T = 2π v / r

Answer: (B)

In circular motion, speed is distance per unit time, and one full revolution covers the circumference 2πr. So the velocity is v = (2πr)/T. To solve for the period T, multiply both sides by T and then divide by v: vT = 2πr, so T = (2πr)/v. This shows that the period grows with the circumference and shrinks as speed increases. The units also line up: meters divided by meters per second gives seconds. Forms like v/(2πr) or r/v or 2πv/r don’t match both the algebra and the units, so they’re not correct.