Question

Starting from rest, a disk rotates about its central axis with constant angular acceleration. In 4.00 s, it rotates 13.2 rad. During that time, what are the magnitudes of (a) the angular acceleration and (b) the average angular velocity? (c) What is the instantaneous angular velocity of the disk at the end of the 4.00 s? (d) With the angular acceleration unchanged, through what additional angle (rad) will the disk turn during the next 4.00 s?

Answer 1

Solution:-

Given:-

In 4.00 s disk rotated 13.2 rad.

a)      Calculate acceleration

Let a be the angular acceleration

ω (t) = at² : 0.5at²

At, t = 4s, at – 13.2rad

a = 2*13.2 / 4²

a = 1.65 rad/s²

The angular acceleration is = a = 1.65 rad/s²

b)     Calculate Average angular velocity as,

Averω (t) = 13.2 / 4.00 = 3.3 rad/s

The average angular velocity is Averω (t) 3.3 rad/s

     c)    Instanteneous Angular velocity of the disk at the end of the 4.00s?

            ω (t) = a*s = 1.65rad/s *4.00s = 6.6rad/s

            ω(t) = 6.6rad/s

   Instanteneous Angular velocity of the disk at the end of the 4.00s is ω(t) = 6.6rad/s

d)     Calculated additional angle ,

ϴ = ω (t) +1/2*at²

ϴ = 6.6 + ½*(1.65)*(4.00s)²

ϴ = 19.8 rad

ϴ = 19 radian

The additional angle is 19 radian.