Question

The angular velocity w of a particle varies with time
tas w = 5t2 + 25 rad/s. The angular acceleration
of the particle at t = 1 s is
(1) 10 rad/s2
(2) 5 rad/s2
(3) Zero
(4) 3 rad/s2​

Answer 1

Differentitate the equation wrt time

On differentiation ,

α= 10t

On putting t=1

α=10 rad/s^2

Option (2)

Answer 2

Answer:

The angular acceleration of the particle at t=1s is    $10rad/s^{2}$

Explanation:

Angular Acceleration:

• Angular acceleration usually denoted by '$\alpha$' is the rate of change of angular velocity.
• It is analogous to that of linear acceleration.
• Mathematically, it is given by

                                           $\alpha=\frac{d\omega}{dt}$

Step 1:

Given:                               $\omega=(5t^{2} +25) rad/s$

Differentiating the equation w.r.t time we get,

                                        $\frac{d\omega}{dt}=5\frac{d(t^{2} )}{dt} \\\frac{d\omega}{dt}=5.2t\\\frac{d\omega}{dt}=10t$

Step 2:

We have to find angular acceleration at t=1s,

                                        $\alpha=\frac{d\omega}{dt}\\\alpha=5t$

Substituting for t,

                                       $\alpha=10(1)\\\alpha=10rad/s^{2}$

The angular acceleration of the particle at t=1s is    $10rad/s^{2}$