Math  /  Algebra

Question5. A wheel has a diameter of 80 cm and completes a revolution in 0.5 seconds at top speed.[4 marks] a) Determine the angular velocity, ω\omega, in radians per second. ω=2π5.5s=4πroρ\omega=\frac{2 \pi}{5.5 s}=4 \pi r o \rho^{\circ} b) How far does the wheel travel in one minute?

Studdy Solution
Calculate the distance traveled by the wheel in one minute.
First, find the circumference of the wheel, which is the distance traveled in one complete revolution. The formula for circumference CC is:
C=π×diameterC = \pi \times \text{diameter}
Given the diameter is 80 cm:
C=π×80=80π cmC = \pi \times 80 = 80\pi \text{ cm}
Next, calculate the number of revolutions in one minute. Since the wheel completes one revolution in 0.5 seconds, the number of revolutions per second is:
Revolutions per second=10.5=2\text{Revolutions per second} = \frac{1}{0.5} = 2
Therefore, the number of revolutions in one minute (60 seconds) is:
Revolutions in one minute=2×60=120\text{Revolutions in one minute} = 2 \times 60 = 120
Finally, calculate the total distance traveled in one minute:
Distance traveled in one minute=120×80π=9600π cm\text{Distance traveled in one minute} = 120 \times 80\pi = 9600\pi \text{ cm}
The distance the wheel travels in one minute is:
9600π cm\boxed{9600\pi \text{ cm}}

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