Question

A small steel roulette ball rolls ccw around the inside of a 30−cm diameter roulette wheel. The ball completes 2.0 rev in 1.20 s. What is the ball's position at t=2.5 s?

Answer 1

The angular velocity of the ball is 5.24 rad/s. The position of the ball at t=2.5 s is approximately 13.1 radians.

Step-by-step explanation:

Given that the ball completes 2.0 revolutions in 1.20 seconds, we can find its angular velocity using the formula:

Angular velocity = (2 * π radians) / (1.20 s)

Plugging in the values, we get:

Angular velocity = (2 * 3.14 radians) / (1.20 s)

Angular velocity ≈ 5.24 rad/s

To find the ball's position at t=2.5 s, we need to find the angle it has traveled.

Since we know the angular velocity and time, we can use the formula:

Angle = Angular velocity * Time

Plugging in the values, we get:

Angle = 5.24 rad/s * 2.5 s

Angle ≈ 13.1 radians