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# If a wheel 1.2m in diameter rotates at one revolution per second

Table of Contents

## Question

If a wheel 1.2m in diameter rotates at one revolution per second. Calculate the velocity of the wheel.

## Answer

The velocity of the wheel is 3.8 meters per second

### Explanation

Data: Revealed information from the question

Diameter of the wheel, d = 1.2 m

Revolution = one (1) = 3600 = 2 x 1800 = 2 x π = 2π radians

Time for one revolution, t = 1 second

Unknown: Unrevealed information from the question

Radius of the circle, r = ?

Angular velocity, ω = ?

Linear velocity, V = ?

Formula: The equation that will help us solve the problem

Step 1: To find the radius of the circle, we will apply the equation below

r = d/2

Step 2: We will use the formulae below to calculate the angular velocity

ω = θ / t

Step 3: We can use the formulae below to calculate the Linear velocity

V = ωr

#### Solution

Step 1: To calculate the radius of the circle, i will the formula

r = d / 2 = 1.2 / 2 = 0.6 m

Therefore, we have the radius of the circle as 0.6 meters

Step 2: In this step, we will use the formula  ω = θ / t to find the angular velocity

ω = θ / t = 2π / 1 = 2 x 3.142 / 1 = 6.28 rad/s

Hence, the angular velocity is 6.28 radians per second

Step 3: We will now insert the relevant data into V = ωr to obtain the Linear velocity of the wheel.

V = ωr = 6.28 x 0.6 = 3.8 m/s

Therefore, the linear velocity is 3.8 meters per second.

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