Question

Suppose a roulette wheel is spinning at 1rev/s. How much time does it take for the wheel to come to rest if its constant angular acceleration is −0.80rad/s^2?

Answer 1

The roulette wheel takes approximately 7.85 seconds to come to rest.

Step-by-step explanation:

To calculate the time it takes for the roulette wheel to come to rest, we can use the formula:

ωf = ωi + αt

Where ωf is the final angular velocity, ωi is the initial angular velocity, α is the angular acceleration, and t is the time. In this case, ωf is 0 since the wheel comes to rest. ωi is 2π radians since the wheel is spinning at 1 revolution per second. α is -0.80 rad/s². So, the formula becomes:

0 = 2π - 0.80t

Simplifying the equation, we get:

t = (2π / 0.80)

Plugging in the values, we find that it takes approximately 7.85 seconds for the roulette wheel to come to rest.