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# Kinematics of Rotational Motion About a Fixed Axis

#### notes

Kinematics of Rotational Motion about a Fixed Axis

We can derive equation of motion similar to translational motion

The kinematical quantities in rotational motion, angular displacement ( θ ), angular velocity ( ω ) and angular acceleration ( α ) respectively are analogous to kinematic quantities in linear motion, displacement (x), velocity (v) and acceleration (a). We know the kinematical equations of linear motion with uniform (i.e. constant) acceleration:

"v" = "v"_"o" +"at"

x = x_o + "v"_"o" "t" + 1/2"at"^2

"v"^2 = "v"_0^2 + 2ax

where x0 = initial displacement and v0 = initial velocity. The word ‘initial’ refers to values of the quantities at t = 0

The corresponding kinematic equations for rotational motion with uniform angular acceleration are:

omega = omega_0 +alpha"t"

theta = theta_0 + omega_0t +1/2alphat^2

omega^2 = omega_0^2 + 2alpha(theta - theta_0)

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