# Change equations from linear motion to rotational motion.

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### 2 Answers

The equations in linear motion are

displacement x = x1- x0

velocity v = (x1- x0)/ (t1-t0) or dx/dt

acceleration a = (v1-v0)/ (t1- t0) or dv/dt or dv^2/ dt^2

(Here the linear position is expressed in terms of metres)

For rotational motion the same equations become

Angular motion T = T1- T0

Angular velocity V = (T1- T0)/ (t1- t0) or dT/dt

Angular acceleration A = (V1 - V0)/ (t1- t0) or dV/dt or dT^2/ dt^2

(Here the angular position is expressed in radians)

In short, just use the angular position instead of the linear position for all the equations.

The relations for velocity, acceleration, instantaneous velocity, instantaneous acceleration, etc. convert easily from linear motion to rotational motion once you have replaced linear position with angular position.

We'll start from the equations of linear motions and we'll write the equivalent equations of rotational motion.

The equation of **velocity in linear motion **is:

**v = ds/dt**

ds is the change of location

dt is the change in time

The equation of **angular speed in rotational motion **is:

**omega = d theta/ dt**

d theta is the change in angular displacement (measured in radians)

dt is the change in time

The equation of **acceleration in linear motion **is:

a = dv/dt

dv change in velocity

**a = v0(t - t0) + a(t-t0)^2/2**

v0 is the original velocity

t is the end time

t0 is the original time

The equation of **angular acceleration in rotational motion **is:

**alfa = d omega/dt**

d omega is the change in angular speed

**theta = omega0(t-t0) + alfa(t-t0)^2/2**