## 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) = 360^{0} = 2 x 180^{0} = 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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