# Circular motion. Uniform and accelerating. (Bridge)

• EVriderDK
In summary, the conversation discusses the process of finding the acceleration and angular velocity of a bridge opening from 0 to 80 degrees. The method involves using three equations with three unknowns and solving for t, which gives the correct answer for acceleration. The person asking for help is unsure of how to determine which equations to use and how to set them up. The responder explains that the equations must contain the given variables and the variable being solved for.
EVriderDK

## Homework Statement

A bridge takes 2 minutes to open up fully from 0 to 80 degrees. The first 20 degrees it is accelerating, and the last 60 degrees it is traveling with even velocity.

I will have to find acceleration for the first 20 degrees and angular velocity for the last 60 degrees.

## The Attempt at a Solution

I have tried setting up three equations with three unknowns:

I have tried isolating a in the first two equations, and then put 1=2. Then isolating ω in this new equation, and replacing this with the ω in the third equation. Then i isolate t, and get 48 second. This gives the correct answer to the acelleration, but i don't know why. Can you help?

Is there other way to do it maybe?

Last edited:
Hi EVriderDK!

That looks ok … you eliminated α, then you solved for t, that is the way to do it.
EVriderDK said:
…This gives the correct answer to the acelleration, but i don't know why.

I don't understand. If it solves the equations, isn't that enough justification?

Why is it correct to use these three equations. I didn't come up with them my self.
I was just told that this i s the correct way to do it, but i lack the understanding.

EVriderDK said:
… I didn't come up with them my self.

ah!

ok, first, are you familiar with the standard constant acceleration equations for ordinary (linear) motion?

Yes I'm familiar with all the formulas, i just cannot see, how the person who put them together, knew, that this was the way to do it.

if a is constant …

then dv/dt = a, so ∆v = at

d2x/dt2 = a, so ∆x = vot + 1/2 at2

a = dv/dt = dv/dx dx/dt = vdv/dx = 1/2 d(v2)/dx, so ∆(v2) = 2as

But how did he know, that I had to use these three equations, in that order etc. ?

Argh! :D

Let me rephrase.

How to find out how many equations you are going to work with, and what these equations have to contain?

it's always obvious which one to use …

it's the one that has the variables you're given, and the variable you want

one has s u a and t

one has u v a and s

one has u v a and t​

So because i don't have ω in the first equation, i have to have an equation with ω in it? Because the third equation needs this ω ?

## What is circular motion?

Circular motion refers to the movement of an object along a circular path or trajectory. This type of motion can be uniform, meaning the object moves at a constant speed, or it can be accelerating, meaning the object's speed changes at a constant rate.

## What is uniform circular motion?

Uniform circular motion is when an object moves along a circular path at a constant speed. This means that the object covers equal distances in equal time intervals, and its velocity is always tangent to the circle.

## What is accelerating circular motion?

Accelerating circular motion is when an object moves along a circular path and its speed changes at a constant rate. This means that the object's velocity vector is constantly changing, and it is always directed towards the center of the circle.

## What is the difference between uniform and accelerating circular motion?

The main difference between uniform and accelerating circular motion is that in uniform circular motion, the speed of the object remains constant, while in accelerating circular motion, the speed of the object changes at a constant rate. Additionally, in uniform circular motion, the object's velocity is always tangent to the circle, while in accelerating circular motion, the object's velocity is always directed towards the center of the circle.

## How is circular motion related to bridges?

Circular motion is often used to describe the movement of objects on bridges, such as cars or trains. Bridges are typically designed to withstand the forces of circular motion, as the vehicles moving on them often follow curved paths. Additionally, the concept of uniform and accelerating circular motion is important in understanding the stability and safety of bridges.

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