How to find Angular Speed when given frequency?

I made a mistake. The correct answer is 0.372 rad/s. In summary, to find the average angular speed of a bike riding around a floral clock in Japan with a radius of 15.5 m and making 16.0 revolutions in 4.50 min, you would use the formula ω = velocity/radius and 1 rev = 2*pi rad. This results in an average angular speed of 0.372 rad/s.
  • #1
Fernando Calvario
13
1

Homework Statement


A floral clock in Japan has a radius of 15.5 m. If you ride a bike around the clock, making 16.0
revolutions in 4.50 min, what is your average angular speed?

Homework Equations


ω = velocity/radius ; 1 rev=2*pi rad

The Attempt at a Solution


(16 rev*2*pi rad)/270 secs = 0.372 rad/s ...Not sure about this since I don't know what to do with the r
 
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  • #2
Hi Fernando Calvario and welcome to PF.

Fernando Calvario said:
(16 rev*2*pi rad)/270 secs = 0.372 rad/s ...Not sure about this since I don't know what to do with the r
Do nothing with r. You have answered the question.
 
  • #3
I get a slightly different answer. Where did the value of the divisor come from in your formula?
 
  • #4
4.5minutes*60 secs
 
  • Like
Likes Tom.G
  • #5
Oops, my mistake. You are right.
Sorry.
 

1. What is angular speed?

Angular speed is a measure of how fast an object is rotating around a central axis. It is usually measured in radians per second (rad/s) or degrees per second (deg/s).

2. How is angular speed different from linear speed?

Angular speed is a measure of rotational motion, while linear speed is a measure of straight-line motion. Angular speed takes into account the distance from the axis of rotation, while linear speed does not.

3. How is frequency related to angular speed?

Frequency is the number of rotations or cycles per unit of time, while angular speed is the rate at which an object is rotating. The higher the frequency, the faster the object is rotating and the higher the angular speed will be.

4. What is the formula for finding angular speed when given frequency?

The formula for finding angular speed when given frequency is angular speed = 2π x frequency. This formula assumes that the units for frequency are in hertz (Hz) and that angular speed is measured in radians per second (rad/s).

5. Can angular speed be negative?

Yes, angular speed can be negative. A negative angular speed indicates that the object is rotating in the opposite direction from the chosen positive direction. The magnitude of the angular speed remains the same regardless of the direction of rotation.

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