# Solve Angular Velocity & Acceleration - Dimensional Analysis

• etile
In summary, the conversation revolves around solving a problem involving linear and angular velocity and acceleration. The participants are discussing the given values and formulae to use in order to arrive at the correct answer. They also highlight the importance of understanding the question and breaking it down into smaller, more manageable parts.
etile
Homework Statement
university
Relevant Equations
n/a
Hi guys,

Please see attached image - it's the part highlighted yellow that I'm stuck on.

Here is what I got for linear velocity and angular velocity. (requested by mod)

Thanks!
c) Angular to velocity
v (linear velocity) = r (radius of circle) * omega (angular velocity)
lets rearrange
linear velo (2.214 m/s = 0.4m* angular)
2.214 / 0.4

d) Angular acceleration of the drum
initial angular velo = 0
final angular veloc=5.535
time=0.225756
formula=
angular acceleration = initial angular velo. (0) - final angular acc. (5.535) / t (0.225756)

Last edited by a moderator:
PF rules require you to provide your own efforts. What are your thoughts on the part of the problem you are asking about?

topsquark
Sorry I didn't realise that.

I pretty much don't understand the question and where to go with it

Before you get onto the 'hard' part of the question, you will need to deal with the ‘easy’ parts, a) – f), correctly.

Ask yourself: “If A (the time taken) is very large, would I expect different answers compared to A being very small?”.

E.g. imagine A = 3600s and then imagine again with A = 1s).

Lnewqban and topsquark

## What is angular velocity and how is it measured?

Angular velocity is a measure of the rate of rotation of an object around a specific axis. It is usually denoted by the Greek letter omega (ω) and is measured in radians per second (rad/s). Angular velocity can also be expressed in degrees per second or revolutions per minute (RPM), but radians per second is the standard unit in physics.

## How do you calculate angular acceleration?

Angular acceleration is the rate of change of angular velocity over time. It is denoted by the Greek letter alpha (α) and is measured in radians per second squared (rad/s²). The formula for angular acceleration is α = Δω / Δt, where Δω is the change in angular velocity and Δt is the change in time.

## What is the dimensional formula for angular velocity?

The dimensional formula for angular velocity is [T^(-1)]. This is because angular velocity is defined as the angle rotated per unit time. Since angle (measured in radians) is dimensionless, the only dimension involved is time, which is in the denominator, giving it the dimension of inverse time.

## How can dimensional analysis be used to verify equations involving angular velocity and acceleration?

Dimensional analysis involves checking that both sides of an equation have the same dimensions. For example, if you have an equation involving angular velocity (ω) and time (t), you can verify it by ensuring that the dimensions on both sides match. For instance, if ω = θ / t (where θ is the angle in radians), the dimensions would be [T^(-1)] = [θ] / [T], confirming that the dimensions are consistent.

## What are common mistakes to avoid in solving problems related to angular velocity and acceleration?

Common mistakes include confusing linear and angular quantities, not converting units appropriately (e.g., degrees to radians), and neglecting to check the consistency of dimensions in equations. It's also important to clearly distinguish between angular velocity (ω) and angular acceleration (α) and to apply the correct formulas for each.

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