# Thread: Linear Velocity and Angular Velocity

1. ## Linear Velocity and Angular Velocity

Two flywheels with diameters of 40 in and 60 in are driven by a moving belt. Find the speed of the belt in feet per second, and find the angular velocity of the larger wheel in revolutions per minute when the smaller wheel makes 48 rpm.

2. ## Re: Linear Velocity and Angular Velocity

Originally Posted by joshuaa
Two flywheels with diameters of 40 in and 60 in are driven by a moving belt. Find the speed of the belt in feet per second, and find the angular velocity of the larger wheel in revolutions per minute when the smaller wheel makes 48 rpm.
First, please show us what you have been able to do. It will allow us to help you better.

Thoughts to ponder: The linear speed of the belt will be the same for both flywheels, otherwise the belt would bunch up on one or the other flywheels. Also the linear speed of a point on the wheel is given by $v = r \omega$.

See what you can do with this. If you are still having problems, feel free to post. (But show your work this time!)

-Dan

3. ## Re: Linear Velocity and Angular Velocity

Thank you topsquark for passing by.

All problems that we have been given by the instructor involved only 1 fly wheel. Therefore, this problem will not be answered properly if I followed 1 wheel strategy as I guess. I will try.

I have more information for the smaller flywheel, so I will take them.

v = rw
= 20 in (48 r/min)

I think now I cannot multiply unless I get rid of Revolutions. Also I will convert minute to second.

= 20 in (48 r/min) (2Pi / r) (min / 60 s)
= 40Pi in (48 / 60 s)
= 4Pi in (48 / 6 s)
= 2Pi in (48 / 3 s)
= 96Pi in / 3 s
= 32Pi in/s

4. ## Re: Linear Velocity and Angular Velocity

Originally Posted by joshuaa
Thank you topsquark for passing by.

All problems that we have been given by the instructor involved only 1 fly wheel. Therefore, this problem will not be answered properly if I followed 1 wheel strategy as I guess. I will try.

I have more information for the smaller flywheel, so I will take them.

v = rw
= 20 in (48 r/min)

I think now I cannot multiply unless I get rid of Revolutions. Also I will convert minute to second.

= 20 in (48 r/min) (2Pi / r) (min / 60 s)
= 40Pi in (48 / 60 s)
= 4Pi in (48 / 6 s)
= 2Pi in (48 / 3 s)
= 96Pi in / 3 s
= 32Pi in/s
Good job. This is the linear speed of a point on the smaller wheel, which must be the same as the speed of the belt if there is to be no slipping. So you are done!

-Dan

5. ## Re: Linear Velocity and Angular Velocity

Thanks for the following.