Question

After 13.4 s, a spinning roulette wheel has slowed down to an angular velocity of 2.84 rad/s. During this time, the wheel has an angular acceleration of -6.52 rad/s^2. Determine the angular displacement of the wheel.

a) 38.128 rad
b) 45.384 rad
c) 21.572 rad
d) 9.268 rad

Answer 1

The angular displacement of the wheel is approximately 38.128 rad. (option a).

Step-by-step explanation:

To determine the angular displacement of the wheel, we can use the equation:

θ = ωit + 0.5αt2

where θ is the angular displacement, ωi is the initial angular velocity, α is the angular acceleration, and t is the time interval. Plugging in the given values, we have:

θ = (0)(13.4) + 0.5(-6.52)(13.4)2

θ ≈ -38.128 rad

Since angular displacement cannot be negative, the correct answer is approximately 38.128 rad (option a).