Starting from rest, a disk rotates about its central axis with constant angular acceleration. In 5.00 s, it rotates 10.1 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 5.00 s? (d) With the angular acceleration unchanged, through what additional angle (rad) will the disk turn during the next 5.00 s?

a

The angular acceleration is  

b

The average angular velocity is

c

The instantaneous angular velocity is  

d

The additional angle (rad) will the disk turn during the next 5.00 s is

Explanation:

From the question we are told that

    The duration of rotation is  

     The angular displacement is  

From newtons Law the angular displacement is mathematically represented as

Where is the angular acceleration  

            is the initial angular velocity and its value is  0

     Making the subject of formula

Substituting value  

The average angular velocity is mathematically represented as

   Substituting value  

From the equations of motion  the instantaneous  angular velocity is mathematically represented as  

Substituting value  

Modifying the equation for angular displacement is mathematically represented as

From the question is not changed

                                t = 5s

  the initial velocity would be the instantaneous velocity

     So  

Substituting value

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explanation: