Adisk rotates about its central axis starting from rest
andaccelerates with constant angular acceleration. at onetime it is
rotating at 10rev/s; 60 rrevolutions later, its angularspeed is
15rev/s. calculate a) the angular acceleration b)thetime required
to complete the 60 revolutions, c) the time requiredto reach the
10rev/s angular speed, and d) the number ofrevolutions from rest
until the time the disk reaches the 10rev/sangular speed.

a  α = 6.54 rad / s², b  t = 4.81 s , c  t = 9.62 s , d    θ = 48.12 rev

Explanation:

We can solve this exercise using angular kinematics

Let's reduce the magnitudes to the SI system

      w₀ = 10 rev / s (2π rad / 1 rev) = 20π rad / s

      = 15 rev / s = 30π rad / s

      θ = 60 rev (2π rad / 1rev) = 120π rad

a)     ² = w₀² + 2 α θ

       α = (wf² - w₀²) / 2 θ

       α = (30²pi² - 20² pi²) / 2 120 pi

      α = 2.08π rad / s²

      α = 6.54 rad / s²

b)     = w₀ + α t

         t = ( - w₀) / α

         t = (30π -20ππ) /2.08π

         t = 4.81 s

c) the time to reach the speed of wf = 20pi rad / s from rest w₀ = 0

        t = (20π -0) /2.08π

        t = 9.62 s

d) the revolutions to reach this speed

         θ = w₀ t + ½ alf t²

         θ = ½ 2.08 pi 9.62²

         θ = 302.37 rad

Let's reduce to revolutions

           θ = 302.37 rad (1 rev / 2pi rad)

           θ = 48.12 rev

total distance travelled = 60 miles

total time taken =1.5 hours

average speed = total distance / total time

60 / 1.5

= 40

therefore, average speed = 40 m/h

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