Determine the dimensions of angular speed $\omega$ .
Some of the equations involving related quantities are
$\omega = \dfrac{\theta_2 - \theta_1}{t_2 - t_1}$ , $\alpha = \dfrac{\omega_2 - \omega_1}{t_2 - t_1}$ , $\Gamma = F \cdot r$ and $I = mr^2$ .
The symbols have standard meanings.

Question

Determine the dimensions of angular speed

\omega

.
Some of the equations involving related quantities are

\omega = \dfrac{\theta_2 - \theta_1}{t_2 - t_1}

,

\alpha = \dfrac{\omega_2 - \omega_1}{t_2 - t_1}

,

\Gamma = F \cdot r

and

I = mr^2

.
The symbols have standard meanings.

Quantrex Academy · Accepted Answer

Correct answer: C. T^ -1

Angular speed ω is given by the relation ω = (θ_2 - θ_1)/(t_2 - t_1) . Angular displacement θ is the ratio of arc length to radius, making it a dimensionless quantity. Its dimensional formula is M^0 L^0 T^0 . Time t has the dimensional formula T . Substituting the dimensions into the equation for angular speed: [ω] = (M^0 L^0 T^0)/(T) = T^ -1

Determine the dimensions of angular speed ω . Some of the equations...

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