Question

An object starts to rotate about an axis from rest wih a, uniform angular acceleration of 2pi rads-2 what is the no.of rotations it can complete in 5s

Answer 1

θ = 12.5 rotations

Step-by-step explanation:

The number of rotations can be found by using the second equation of motion:

`\theta = \omega_i t + (1)/(2)\alpha t^2\\\\`

where,

`\theta` = angular displacement = ?

ωi = initial angular speed = 0 rad/s

t = time = 5 s

α = angular acceleration = 2π rad/s²

Therefore,

`\theta = (0\ rad/s)(5\ s)+(1)/(2)(2\pi\ rad/s^2)(5\ s)^2\\\\\theta = 78.54\ rad`

converting it to no. or rotations:

`\theta = (78.54\ rad)((1\ rotation)/(2\pi\ rad))`

θ = 12.5 rotations