(The number of times a bicycle tire rotates in a given time period is directly related to the distance traveled in that time period. Consider the following scenarios.)
1. Calculate the angular speed of a bike with 26-inch tires rotating at 200 revolutions per minute. Express your answer in radians per minute. Use π = 3.14.
Here's what I got:
angular speed= (200 revs•2π/60 radians per second) =20.94 radians per second
(20.94 radians/second)•(60 sec/1 min)= 1256.4 radians per minute
Is this correct?? Thank you and Happy New Year!
the wheel rotates 200 time per minute
1 rotation is 2π radians , so
= 200(2π) radians/min
= 400π radians/min = appr 1256.6 radians/min
you are correct
notice that the length of the radius has nothing to do with the angular velocity.
Thanks!
Yes, your calculation is correct!
To calculate the angular speed of the bike in radians per minute, you first need to convert the number of revolutions per minute to radians per second. One revolution is equivalent to 2π radians, and there are 60 seconds in a minute. So, you can multiply the number of revolutions per minute by (2π/60) to convert it to radians per second.
In this case, the bike is rotating at 200 revolutions per minute. Thus, the angular speed can be calculated as follows:
Angular speed = (200 revs) * (2π/60 radians per second) = 20.94 radians per second.
To convert this to radians per minute, you can multiply it by 60 seconds per minute:
Angular speed = 20.94 radians per second * 60 seconds per minute = 1256.4 radians per minute.
So, the angular speed of the bike with 26-inch tires rotating at 200 revolutions per minute is indeed 1256.4 radians per minute.
Happy New Year to you too! If you have any more questions, feel free to ask.