Question

A particle moves along the circular path of radius 15 cm with a constant angular acceleration of 4 Radian per second square if the initial angular speed of the particle is 5 Radian per second find angular displacement of the particle in 5 second. ​

Answer 1

Answer:

$\frac{dw}{dt} = 4 \\ w = \int4dt = 4t + c$

at t = 0 angular velocity is 5 So 5 = 0 + c or c = 4 .

Again integrate

$\theta = 2 {t}^{2} + 4t$

*(let t = 0 , displacement 0)

Now at t = 5

$\theta = 2 \times 25 + 4 \times 5 = 70rad$

So displacement

$s = r \theta = 15 \times 70cm = 10.5m$