A point on a fan blade sits 0.30 m from the hub. The fan turns steadily, one revolution every 0.50 s.
What is the point's speed, in m/s?
The point's circle has radius r = 0.30 m, and one revolution takes T = 0.50 s, at a steady speed.
In one revolution, the point's distance is one circumference, 2 × π × 0.30 m. The time is 0.50 s.
Speed is distance traveled divided by the time taken. That is all the speed formula is.
This is not a new speed formula. It is speed = distance ÷ time, written for one revolution: distance 2πr, time T.
With r in meters and T in seconds, the speed comes out in meters per second.
The relationship holds only while the speed is steady. If the object is speeding up or slowing down around the circle, one number cannot be its speed.
A bigger r makes v bigger, and a bigger T makes v smaller: the two rules you met in the last two lessons are both inside the equation.
An object moves around a circle at a steady speed. Which relationship gives its speed from the radius and the period?
A point on a fan blade sits 0.30 m from the hub, and the fan turns steadily with a period of 0.50 s. Calculate the point's speed.
Write down the values:
r = 0.30 m, T = 0.50 s, v = ?
Write down the equation:
v = 2πr/T
Substitute in the values, and calculate:
v = (2 × π × 0.30) ÷ 0.50 = 3.8
The point moves at 3.8 m/s.
An object moves around a circle of radius 2.0 m at a steady speed, with a period of 4.0 s. Calculate its speed.
Write down the values:
r = 2.0 m, T = 4.0 s, v = ?
Write down the equation:
v = 2πr/T
Substitute in the values, and calculate:
v = (2 × π × 2.0) ÷ 4.0 = 3.1
The object moves at 3.1 m/s: π meters each second.
A toy race car runs a circular slot track at a steady speed: radius 1.5 m, one lap every 2.0 s. Enter the car's speed in m/s, to the nearest 0.1 m/s. Answers within 0.1 m/s are accepted.
In v = 2πr/T, the radius r is in meters and the period T is in seconds. Which unit does the speed v come out in?
A horse on a carousel moves at a steady speed on a circle of radius 5.0 m, with a period of 4.0 s. Enter the horse's speed in m/s, to the nearest 0.1 m/s. Answers within 0.1 m/s are accepted.
A ride platform turns steadily. Fergus sits 3.0 m from the center, each full turn takes 12 s, the whole ride lasts 180 s, and the platform is 6.0 m across. Which value plays the part of T in v = 2πr/T?
Elif rides her bicycle at a steady speed around a circular path of radius 25 m, completing each lap in 40 s. Enter her speed in m/s, to the nearest 0.1 m/s. Answers within 0.1 m/s are accepted.