Question

A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest, it reaches 100 revs/second in 4 seconds.Find the angular acceleration ? Find the angle rotated during these four seconds.

Answer 1

Given in the question :-
t = time = 4 s.
Initial angular velocity,ω₀  = 0
Final angular velocity,ω' =100 revs/s .
α = angular acceleration 

We know the formula,
 ω' = ω₀ + αt

100 = 0 + α x 4

α =100/4
α = 25 rev/s².
Here, The angle rotated into three equation of kinematics . 

$\theta = \omega t+ \frac{1}{2} \alpha t^2$
= $0 + \frac{1}{2} * 25 * 4^2$
=8 x 25
= (200 x 2 π)
=400 π radians.


Hope it Helps :-)

Answer 2

The angular acceleration is α = 25 rev/s².

The angle rotated during these four seconds is 400 π radians.

Explanation:

Given values :

                      t = time = 4 s.

                      ω₀  = 0

Formula :           ω' = ω₀ + αt

Where,           ω₀  is Initial angular velocity

                      ω' = 100 revs/s .

                      ω' is Final angular velocity  

                      α = angular acceleration  

We are aware of the formula,

                        ω' = ω₀ + αt

                       100 = 0 + α x 4      

                          α = 100/4

                          α = 25 rev/s².                    

There, the angle transformed into three kinematics equations.

                            $\theta=w t+\frac{1}{2} \alpha t^{2}$

                            $\theta=0+\frac{1}{2} \times 25 \times 4^{2}$

                            $\theta=\frac{1}{2} \times 25 \times 16$

                             $\theta=25 \times 8$          

                                = 200                  

In radian,      

                    =200×2π      

                    =400 π radians.

Therefore, the angular acceleration is α = 25 rev/s² and the angle rotated during those four seconds is 400 π radians.