Final answer:
The wheel turns through an angle of 40 rads in 5 seconds. Therefore, the correct option is d. 40 rads.
Step-by-step explanation:
The question involves a wheel slowing down from 20 rad/s to 12 rad/s in 5 seconds due to the action of a constant frictional torque. To find the angle through which the wheel has turned, we can use the concept of angular displacement in uniformly accelerated rotary motion.
The formula for angular displacement θ, when an object decelerates at a constant rate, is given by θ = ωi * t + ½ * α * t², where ωi is the initial angular velocity, t is the time, and α is the angular deceleration.
To find the angle turned by the wheel, we can use the formula:
θ = ω₀t + (1/2)αt²
where θ is the angle turned, ω₀ is the initial angular velocity, α is the angular acceleration, and t is the time taken.
Given that the wheel slows from 20 rad/s to 12 rad/s in 5 s, we have:
ω₀ = 20 rad/s, ω = 12 rad/s, and t = 5 s.
Substituting these values into the formula, we can calculate the angle turned by the wheel:
θ = (20 rad/s)(5 s) + (1/2)(-8 rad/s²)(5 s)² = 40 rad.