Question

w= theta/time
w/t = theta/time squared
dw/dt= dtheta/d time squared
a=dtheta/d time squared
where w is angular velocity and a is angular acceleration.
But this is wrong! a= d SQUARED theta/d time squared?

Answer 1

Answer on Question #53484-Physics-Mechanics-Kinematics-Dynamics

w= theta/time

w/t = theta/time squared

dw/dt= dtheta/d time squared

a=dtheta/d time squared

where w is angular velocity and a is angular acceleration.

But this is wrong! a= d SQUARED theta/d time squared?

Solution

Angular velocity is

$$\omega = \frac {d \theta}{d t} \neq \frac {\theta}{t}.$$

Angular acceleration is

$$\alpha = \frac {d \omega}{d t} = \frac {d}{d t} \left(\frac {d \theta}{d t}\right) = \frac {d ^ {2} \theta}{d t ^ {2}}.$$

In addition we never use unpaired $d$ in the formulas for derivatives. We cannot use formulas such as

$$\alpha = \left(\frac {d \theta}{d t ^ {2}}\right).$$

If $t^2$ is our variable we can write

$$\alpha = \left(\frac {d \theta}{d (t ^ {2})}\right)$$

when we use first derivative of $\theta$ by $t^2$ .

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