A spinning wheel steadily slows from an initial angular velocity of 1.65 rev/s to 0.485 rev/s in 12.2 s.

(a) Calculate the wheel's angular acceleration in radians per second squared.
rad/s2

(b) What angle does it go through during that time?
rad

acceleration=(wf-wi)/time

= 2PI(.485-1.65)/12.2

displacement (radian)=avgspeed*time
= 2PI(wf+wi)/2 * 12.2

To calculate the angular acceleration of the spinning wheel, we can use the formula:

Angular acceleration (α) = (final angular velocity - initial angular velocity) / time

So, in this case, we have:
Initial angular velocity (ω1) = 1.65 rev/s
Final angular velocity (ω2) = 0.485 rev/s
Time (t) = 12.2 s

(a) To calculate the angular acceleration (α) in radians per second squared, we need to convert the angular velocities from rev/s to rad/s by multiplying them by 2π (since 1 revolution equals 2π radians).

ω1 = 1.65 rev/s * 2π rad/rev = 10.35 rad/s
ω2 = 0.485 rev/s * 2π rad/rev = 3.048 rad/s

Now we can calculate the angular acceleration:

α = (ω2 - ω1) / t
α = (3.048 rad/s - 10.35 rad/s) / 12.2 s
α = -7.302 rad/s / 12.2 s
α ≈ -0.598 rad/s^2 (rounded to 3 decimal places)

Therefore, the wheel's angular acceleration is approximately -0.598 rad/s^2.

(b) To calculate the angle the wheel goes through during that time, we can use the formula:

θ = ω1 * t + 0.5 * α * t^2

θ = 10.35 rad/s * 12.2 s + 0.5 * (-0.598 rad/s^2) * (12.2 s)^2
θ = 126.27 rad + 0.5 * (-0.598 rad/s^2) * 148.84 s^2
θ ≈ 126.27 rad + (-44.57 rad)
θ ≈ 81.70 rad (rounded to 2 decimal places)

Therefore, the wheel goes through an angle of approximately 81.70 radians during that time.