Question

A wheel is subjected to uniform angular acceleration about its axis.Initally its angular velocity is zero.In the first 2s it rotates about an angle a1, in the next 2s through an additional anglt a2.Then a1/a2

Answer 1

Given:

Angular velocity = 0

Time = 2 seconds at angle a1

Time  = 2 seconds at angle a2

To Find:

a1/a2

Solution:

Let the uniform angular acceleration = α  

and ω0 = 0

a = ω0t + 1/2at²

=  a1 = 0 +1/2 a2² = 2a --- eq 1

Now, let the angular velocity changes to =  ω'

ω' = ω0 + at

= ω' = 0 + a x 2

= ω' = 2a

Now, θ2 = ω't + 1/2at² = 2a.2 + 1/2a2² = 6a --- eq 2

Now, from eq 1 and 2

= a1/a2 = 6a/2a

= 3

Answer: Thus, the value of a1/a2 is 3.