Rotational motion equations

[pb23me]

Homework Statement

My lab book list these four Rotational motion equations and doesn't say what they are. Could someone please tell me what each equation is and what they are used for. thanx

Homework Equations

$$\theta$$₂-$$\theta$$₁=(w₁+w₂)(t₂-t₁)/2
w₂-w₁=alpha(t₂-t₁)
$$\theta$$₂-$$\theta$$₁=w₁(t₂-t₁)+1/2alpha(t₂-t₁)²
2alpha($$\theta$$₂-$$\theta$$₁)=w₂²-w₁²

The Attempt at a Solution

 

[Delphi51]

The first one isn't correct. The w1 term has different units than the other terms. The second one is analogous to good old ΔV = a*Δt, sometimes written as a = ΔV/Δt. Instead of acceleration, you have rotational acceleration. Instead of velocity, you have rotational or angular velocity.

The third one looks a lot like d = Vi*t + 1/2*a*t², doesn't it?
For the last one, the right side is analogous to Vf² - Vi². Have you seen a formula with that on one side?

 

[pb23me]

ok so am i supposed to use one of these to solve my problem? I am just not sure which equation to use

 

[tiny-tim]

hi pb23me!

My lab book list these four Rotational motion equations and doesn't say what they are. Could someone please tell me what each equation is and what they are used for …

for an object moving in a circle, the usual linear equations may be used with angular acceleration velocity and displacement instead of ordinary (linear) acceleration velocity and displacement (in other words: with α ω and θ instead of a v and t) …

see the PF Library on https://www.physicsforums.com/library.php?do=view_item&itemid=204" for some details

(and you use whichever of those equations contains the variables you are given or are seeking)

 

[rwisz]

The four equations listed are commonly known as the rotational motion equations, which are used to describe the motion of objects that are rotating or moving in a circular path. Each equation relates different variables such as angular displacement (\theta), angular velocity (w), and angular acceleration (alpha) to time (t).

The first equation, \theta2-\theta1=(w1+w2)(t2-t1)/2, is called the average angular displacement equation and is used to calculate the average angular displacement of an object between two points in time.

The second equation, w2-w1=alpha(t2-t1), is known as the average angular velocity equation and is used to calculate the average angular velocity of an object between two points in time.

The third equation, \theta2-\theta1=w1(t2-t1)+1/2alpha(t2-t1)2, is called the displacement equation and is used to calculate the angular displacement of an object at a specific point in time, taking into account its initial angular velocity and acceleration.

The fourth equation, 2alpha(\theta2-\theta1)=w22-w12, is known as the average angular acceleration equation and is used to calculate the average angular acceleration of an object between two points in time.

These equations are essential for understanding and analyzing rotational motion and are commonly used in physics and engineering applications.