Question

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

• A. $600$ rad
• B. $800$ rad
• C. $400$ rad
• D. $200$ rad

Answer 1

The correct option is B $800$ rad

The rotation in this case is divide into three parts , uniform acceleration, uniform rotation without acceleration & at last uniform deceleration.

Time duration $t=10sec.$

angle rotation $=\theta$

Here the rotation in the first and third part will be same.

Hence Total angle rotation,

$=\theta +{\theta }^{\prime }+\theta "$

$=\theta +{\theta }^{\prime }+\theta$ {here $\theta ={\theta }^{\prime \prime }$}

$=2\theta +{\theta }^{\prime }.$----→(a)

We know the equation of kinematics,

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

Put all the values in this equation

$=0\ast 10+(\frac{1}{2}\ast 4\ast 10\ast 10)$

$\theta =200$ radians

Now,

${\theta }^{\prime }={\omega }^{\prime }\ast t$

${\theta }^{\prime }=(\omega +\alpha t)t$

$=(0+4\ast 10)10$

${\theta }^{\prime }=400$ radians

Hence the rotation of total angle , by equation (a)

$=2\theta +{\theta }^{\prime }=(2\ast 200+400)$

$=800rad.$