Question

Obtain following equation from first principles: (i) w= W. + at (ii) q= w.t+ -at

Answer 1

Answer:

For constant angular acceleration we can use kinematic equations as

$\omega = \omega_0 + \alpha t$

$\theta = \omega_0 t + \frac{1}{2}\alpha t^2$

Explanation:

As we know that if angular acceleration is constant then we will have

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

now we have

$d\omega = \alpha dt$

integrate both sides we have

$\int d\omega = \alpha \int dt$

$\omega - \omega_0 = \alpha t$

$\omega = \omega_0 + \alpha t$

ii)

Now from above equation we have

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

so we will have

$\omega_0 + \alpha t = \frac{d\theta}{dt}$

so we have

$d\theta = \omega_0 dt + \alpha t dt$

again integrate both sides

$\int d\theta = \omega_0 \int dt + \alpha \int t dt$

$\theta = \omega_0 t + \frac{1}{2}\alpha t^2$

#Learn

Topic : Kinematics

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