Angular Velocity is defined as change in angular displacement per unit time. Its formula is

Angular Velocity =Angular displacement/Time
Dimensional Formula of Angular displacement= M⁰L⁰T⁰ Divide it by Time T¹

So Dimensional Formula of Angular Velocity = M⁰L⁰T^-1
SI unit of Angular Velocity is rad s^-1

Angular Acceleration is defined as change in angular velocity per unit time . Its formula is

Angular Acceleration = Angular velocity / Time

Dimensional Formula of Angular velocity = M⁰L⁰T^-1 Divide it by Time T¹

So Dimensional Formula of Angular Acceleration = M⁰L⁰T^-2
SI unit of Angular displacement is rad s^-2

Angular Momentum is a product of Moment of Inertia and Angular Velocity. Its formula is
Angular Momentum = Moment of Inertia X Angular Velocity

Dimensional Formula of Moment of Inertia= M¹L²T⁰
Dimensional Formula of Angular velocity = M⁰L⁰T^-1

Putting these values in above equation we get

So Dimensional Formula of Angular Momentum = M¹L²T^-1
SI unit of Angular Momentum is Kg m² s^-1

Angular displacement is defined as the ratio of length and radius.

Angular displacement= Length/Radius
Now we know
Dimensional Formula of Length = M⁰L¹T⁰
Dimensional Formula of Radius  = M⁰L¹T⁰  —- Radius is related to length.

So
Angular displacement= M⁰L¹T⁰/M⁰L¹T⁰

Hence Dimensional Formula of Angular displacement = M⁰L⁰T⁰
SI units of Angular displacement is radian

We have already shown how to calculate Absolute error, mean absolute error, relative error and percentage error in previous posts but the real problem arises when we have two quantities and we need to find out the combined errors.

Here are the formula’s to be used

Lets say we have three quantities a, b and x. The absolute errors in these are respectively + – Δa, + – Δb and + – Δx

Case 1 When x= a+b then Δx= +- [Δa+Δb]
Case 2 When x= a-b then Δx= +- [Δa+Δb]
Case 3 When x= axb then Δx/x= +- [Δa/a+Δb/b]
Case 4 When x= a/b then Δx= +- [Δa/a+Δb/b]

Case 5 When x= aⁿ b^m/ c^o then
Δx/x = +- [nΔa/a+mΔb/b+pΔc/c]