If a wheel 1.2m in diameter rotates at one revolution per second. Calculate the velocity of the wheel.
The velocity of the wheel is 3.8 meters per second
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
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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