# Calculate Angular Velocity of 70cm Bicycle at 25km/hr

• Daaniyaal
In summary, the question asks for the angular velocity in radians per second of a bicycle with tires 70 cm in diameter traveling at 25 km/hr. After converting the speed to cm/sec, the formula v = rω is used to solve for the angular velocity, resulting in 19.8 radians per second. The student initially used a longer method involving division and multiplication by π, but was later reminded of the standard formula.
Daaniyaal

## Homework Statement

A bicycle with tires 70 cm in diameter is traveling along a road at 25 km/hr. What is the angular velocity in radians per second?

A= 1/2r^2 ∅

## The Attempt at a Solution

Nvm I figured it out,

You first convert 25 km/h into cm/sec

25,000,00/60/60 = 694.5
Then, we go 2pi * 35 which gives us 219.8
We then divide 694/219.8

Which gives us 3.16

We multiply 3.16 with 2pi

And get 19.8 radians per second.

Last edited:
Hi Daaniyaal!

That's correct, but why did you divide by π and then multiply by it again later?

Using the standard formula v = rω is much easier!

tiny-tim said:
Hi Daaniyaal!

That's correct, but why did you divide by π and then multiply by it again later?

Using the standard formula v = rω is much easier!

Oh! Thanks! I didn't know the formula when I was doing this question, so I had to think it out.

## What is angular velocity?

Angular velocity is a measure of the rate at which an object is rotating or spinning. It is denoted by the Greek letter omega (ω) and is measured in radians per second.

## How do you calculate angular velocity?

Angular velocity can be calculated by dividing the change in angular position (θ) by the change in time (t). This can be represented by the equation ω = Δθ/Δt.

## What are the units of angular velocity?

The units of angular velocity are radians per second (rad/s) or revolutions per second (rev/s). These units are equivalent, with 1 revolution being equal to 2π radians.

## How does the velocity of a bicycle affect its angular velocity?

The velocity of a bicycle does not directly affect its angular velocity. Angular velocity is determined by the rotational motion of the wheels, which is not directly related to the linear velocity of the bicycle.

## What is the angular velocity of a 70cm bicycle moving at 25km/hr?

The angular velocity of the bicycle depends on the diameter of the wheels. Assuming the diameter of the wheels is 70cm, the angular velocity can be calculated by converting the linear velocity of 25km/hr to meters per second (m/s) and dividing this by the radius of the wheels (35cm). This results in an angular velocity of approximately 6.37 rad/s.

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