Question

A disk with mass m = 9.5 kg and radius r = 0.3 m begins at rest and accelerates uniformly for t = 18.1 s, to a final angular speed of ω = 28 rad/s. 1) what is the angular acceleration of the disk? rad/s2 2) what is the angular displacement over the 18.1 s? rad 3) what is the moment of inertia of the disk? kg-m2 4) what is the change in rotational energy of the disk? j 5) what is the tangential component of the acceleration of a point on the rim of the disk when the disk has accelerated to half its final angular speed? m/s2 6) what is the magnitude of the radial component of the acceleration of a point on the rim of the disk when the disk has accelerated to half its final angular speed? m/s2 7) what is the final speed of a point on the disk half-way between the center of the disk and the rim? m/s 8) what is the total distance a point on the rim of the disk travels during the 18.1 seconds?

Answer 1

Ahhh this going to be confusing sorry...
1. α = Δω / Δt = 28 rad/s / 19s = 1.47 rad/s²

2. Θ = ½αt² = ½ * 1.47rad/s² * (19s)² = 266 rads

3. I = ½mr² = ½ * 8.7kg * (0.33m)² = 0.47 kg·m²

4. ΔEk = ½Iω² = ½ * 0.47kg·m² * (28rad/s)² = 186 J

5. a = α r = 1.47rad/s² * 0.33m = 0.49 m/s²

6. a = ω² r = (14rad/s)² * 0.33m = 65 m/s²

7. v = ω r = 28rad/s * ½(0.33m) = 4.62 m/s

8. s = Θ r = 266 rads * 0.33m = 88 m