Q. 35.0( 2 Votes )

# A wheel starting from rest is uniformly accelerated at 4 rad/s^{2} for 10 seconds. It is allowed to rotate uniformly for the next 10 seconds and is finally brought to rest in the next 10 seconds. Find the total angle rotated by the wheel.

Answer :

Given data –

Acceleration, = 4 rad/s^{2}

Here, three situations come –

1.Intially for 10 seconds uniform acceleration

2.Next, uniform rotation without acceleration for 10 seconds

3. last uniform deceleration for 10 seconds.

Also, the rotation in first and third case remains same.

Hence, total angle of rotation becomes –

Using the second equation of kinematics.

Where,

θ = total angle rotated

= initial angular velocity

t = time period

=angular acceleration

Substituting the values –

radians

We know, angular velocity is related to as-

radians

Hence, the total angle of rotation becomes-

θ_{Total} =400+200+200 = 800radians

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