# Angluar Kinematics

## Homework Statement

A cyclist is traveling at a speed of 30km/hr. If the diameter of the bike wheel is 0.70 meter, what is the angular velocity of the wheels in rad/sec?

## The Attempt at a Solution

Hi, I have racked my brain trying ot work this out, I know the answer is 23.7 rad/sec
(but I don't know hoe to get there ;-(!!
All I could come up with is 0.83m/s=speed and r=0.07m

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Hootenanny
Staff Emeritus
Gold Member

## Homework Statement

A cyclist is traveling at a speed of 30km/hr. If the diameter of the bike wheel is 0.70 meter, what is the angular velocity of the wheels in rad/sec?

## The Attempt at a Solution

Hi, I have racked my brain trying ot work this out, I know the answer is 23.7 rad/sec
(but I don't know hoe to get there ;-(!!
All I could come up with is 0.83m/s=speed and r=0.07m
Welcome to Physics Forums.

The speed of the bicycle is the tangential speed of the wheels (assuming no slipping). So, the question now becomes, how is the tangential speed related to the angular speed of a disc?

okay, not sure if im thinking is on the right track, but would the angular speed be in reference to revolutions/time period? Where 1 revolution - 2(pi)r?

Hootenanny
Staff Emeritus
Gold Member
okay, not sure if im thinking is on the right track, but would the angular speed be in reference to revolutions/time period? Where 1 revolution - 2(pi)r?
Almost, the definition of angular velocity (or speed) should be in your notes or textbook. Perhaps you could look it up.

okay, all it says is angular speed = angular distance / change in time

If the total distance in 30 km = 3000m

r= 0.7m

I really just don't get it sorry.... Im sure its very basic and im missing something here.... ill kick myself when I find out thats for sure !!

Hootenanny
Staff Emeritus
Gold Member
Okay, thankyou for your help.... but im back to sqaure 1 lol.... gawd !!

okay if v=wr and s=2pi and the displacmeent is 2pi (6.8 rad) X 0.70 = 4.40, and v=30km/hr , is the tangential velcoity 0.83m/s

Hootenanny
Staff Emeritus
Gold Member
Okay, thankyou for your help.... but im back to sqaure 1 lol.... gawd !!

okay if v=wr and s=2pi and the displacmeent is 2pi (6.8 rad) X 0.70 = 4.40, and v=30km/hr , is the tangential velcoity 0.83m/s
Not quite. 30 km/hr is 8.33... m/s. So, the equation you need is

$$v = \omega r$$

Now, you have v (8.33 m/s) and you can work out the radius, r. And you need to work out $\omega$. Do you think you can do that?

.... oh dear.... it is 8.3m/s .... no wonder I have spent 1/2 the day try to work it out ..... lol..... told you I would kickmyself.... instead I think i need paperbag lol...