Answer :
Final answer:
The period of the rotation of the wheel is 0.23 seconds, and the tangential speed of the chewing gum stuck on the rim of the wheel is approximately 10.06 m/s.
Explanation:
The question pertains to the theories of circular motion and tangential speed. To answer the question, we first need to find the period of the rotation. By definition, the period is the time for one complete rotation. Given that the wheel rotates 4.35 times every second, we thus have the period as T = 1 / 4.35 = 0.23 seconds.
Next, to find the tangential speed of the chewing gum stuck to the rim of the wheel, we utilise the formula for tangential speed: v = rω, where r is the radius of the wheel and ω is the angular velocity. However, since we are given the number of rotations per second, we can also think of tangential speed as the total path length (or circumference of the wheel) divided by the time. Therefore, v = 2πr/T. Substituting the given values, we get v = 2 * π * 0.369 m / 0.23 s ≈ 10.06 m/s. Thus, the tangential speed of the chewing gum is approximately 10.06 m/s.
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