Question

write down the equation of motion in circular path​

Answer 1

Answer

For motion in a circle of radius r, the circumference of the circle is C = 2π r. If the period for one rotation is T, the angular rate of rotation, also known as angular velocity, ω is:

{\displaystyle \omega ={\frac {2\pi }{T}}=2\pi f={\frac {d\theta }{dt}}\ }{\displaystyle \omega ={\frac {2\pi }{T}}=2\pi f={\frac {d\theta }{dt}}\ } and the units are radians/second

The speed of the object travelling the circle is:

{\displaystyle v={\frac {2\pi r}{T}}=\omega r}{\displaystyle v={\frac {2\pi r}{T}}=\omega r}

The angle θ swept out in a time t is:

{\displaystyle \theta =2\pi {\frac {t}{T}}=\omega t\,}{\displaystyle \theta =2\pi {\frac {t}{T}}=\omega t\,}

The angular acceleration, α, of the particle is:

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

In the case of uniform circular motion, α will be zero.

The acceleration due to change in the direction is:

{\displaystyle a_{c}={\frac {v^{2}}{r}}=\omega ^{2}r}{\displaystyle a_{c}={\frac {v^{2}}{r}}=\omega ^{2}r}