Question 1: If the plate microwave oven has a radius of 0.15 m and rotates at 6.0 rev/min, calculate the total distance traveled by the fly during 2.0 min cooking period.
Explanation: When the plate rotates in the oven, it covers angular displacement θ. However, we want to find the linear distance in the given time of 2.0 min. Now, for one complete revolution of the plate, θ = 2π. Since, the plate takes 6 revolutions in one minute, therefore, angular displacement of the plate in one minute = 6 × 2π = 12π.
Similarly, angular displacement is converted to linear displacement by the formula, S = rθ, where S is the linear displacement.
Given Radius of the plate = 0.15 m
Total time = 2 minutes
No of revolutions per minute = 6
Asked Distance covered, S
Now, angular displacement in 2 minutes = θ = 2 × 12π
To convert this angular displacement into linear displacement, we apply the formula, S = rθ.
Put the values,
S = 0.15 × 2 × 12π = 0.15 × 2 × 12 × 3.14 = 11.304 m ≅ 11 m (Answer)