Question

Write the equations of motion for a particle rotating about a fixed axis?

Answer 1

there are three important equations for a particle rotating about a fixed axis.

1. $\omega=\omega_0+\alpha t$

2. $\theta=\omega_0t+\frac{1}{2}\alpha t^2$

3. $\omega^2=\omega_0^2+2\alpha\theta$

where $\omega_0$ is the initial angular velocity,
$\omega$ is the final angular velocity ,
$\alpha$ is the angular acceleration
and $\theta$ is the angular position of particle after time t.

Answer 2

Hey buddy,

● Kinematics of fixed axis rotation -
The laws of rotational motion and translational motion are analogous to each other.

Consider,
θ = initial angular displacement
ω = initial angular velocity
α = angular acceleration
t = time elapsed
θ' = angular displacement at instant t
ω' = angular velocity at instant t

Now, we can write kinematic eqns of rotational motion as-
1. ω' = ω + αt
2. θ'-θ = ωt + 1/2 αt^2
3. ω'^2 = ω^2 + 2α(θ'-θ)

Hope that is helpful...