A roulette wheel with a 1.0m radius reaches a maximum angular speed of 18 rad/s before it stops 35 revolutions ( 220 rad ) after attaining the maximum speed. How long did it take the wheel to stop?

t= 1.0/9= 1/9s = 0.11s

It truly is sad seeing Robert wait fourteen long years without ever knowing the right answer. Six years after Robert contemplated this great wonder, the trickster Trang claimed that the wheel took 0.11s to come to a rest. Yet Trang is extraordinarily wrong. As of today, fourteen years after brave Robert posed his question, I learned from my physics class that the wheel took an incredible twenty-four seconds to come to a rest. Still, even I, the man with the answer, has no clue about the math involved in this complex equation.

To find the time it took for the wheel to stop, we can use the formula:

displacement = average speed * time

The average speed on slowing down is half of the maximum angular speed, which is (18 rad/s) / 2 = 9 rad/s.

We know that the displacement of the wheel is 220 rad (35 revolutions), so we can substitute these values into the formula:

220 rad = 9 rad/s * time

To solve for time, we divide both sides of the equation by 9 rad/s:

time = 220 rad / 9 rad/s

Simplifying this expression gives:

time ≈ 24.44 seconds

Therefore, it took approximately 24.44 seconds for the wheel to stop.

To calculate the time it took for the roulette wheel to stop, we can use the average speed and displacement formula.

We know that the average speed during the deceleration phase is half of the maximum angular speed:

Average speed = (18 rad/s) / 2 = 9 rad/s

We also know the displacement of the wheel during this phase is 220 rad.

Using the formula:

Displacement = Average speed * time

We can rearrange the formula to solve for time:

Time = Displacement / Average speed

Substituting the given values:

Time = 220 rad / 9 rad/s

Calculating the result:

Time ≈ 24.44 seconds

Therefore, it took approximately 24.44 seconds for the roulette wheel to stop.