Henrik's model train runs a circular track of radius 1.2 m at a steady speed, one lap every 6.0 s.
How fast is the train moving, in m/s?
Henrik's train has r = 1.2 m and T = 6.0 s, and the speed is the unknown.
You have seen the equation: v = 2πr/T, for steady-speed circular motion.
Finding the speed is a routine, and the same three steps work every time.
Step 1: write down the values in the question, and mark the unknown.
Step 2: write down the equation.
Step 3: substitute in the values, and calculate.
The result line always carries its unit: meters per second (m/s).
r is the radius in meters, and T is the time for one revolution in seconds. A diameter must be halved, and a many-lap time must be shared out, before they go in.
Henrik's model train runs a circular track of radius 1.2 m at a steady speed, one lap every 6.0 s. Calculate its speed.
Write down the values:
r = 1.2 m, T = 6.0 s, v = ?
Write down the equation:
v = 2πr/T
Substitute in the values, and calculate:
v = (2 × π × 1.2) ÷ 6.0 = 1.3
The train moves at 1.3 m/s.
A ceiling-fan blade tip sits 0.60 m from the hub, and the fan turns steadily with a period of 0.40 s. Calculate the tip's speed.
Write down the values:
r = 0.60 m, T = 0.40 s, v = ?
Write down the equation:
v = 2πr/T
Substitute in the values, and calculate:
v = (2 × π × 0.60) ÷ 0.40 = 9.4
The tip moves at 9.4 m/s.
A carousel horse circles at a steady speed, 4.0 m from the center, with a period of 8.0 s. Enter its speed in m/s, to the nearest 0.1 m/s. Answers within 0.1 m/s are accepted.
A cyclist rides a circular track of radius 20 m at a steady speed, one lap every 25 s. Enter her speed in m/s, to the nearest 0.1 m/s. Answers within 0.1 m/s are accepted.
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A point on a revolving door panel sits 1.0 m from the central shaft. The door turns steadily with a period of 4.0 s. Enter the point's speed in m/s, to the nearest 0.1 m/s. Answers within 0.1 m/s are accepted.
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Golda's go-kart holds a steady speed on a circular course. Her distance from the course's center is 16 m, and each lap takes 11 s. Enter the go-kart's speed in m/s, to the nearest 0.1 m/s. Answers within 0.1 m/s are accepted.
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