How Do You Calculate Acceleration and Velocity in a Spinning Disk Problem?

[rgalvan2]

Spinning Disk problem. Due tomorrow! Help please!

A disk with a diameter of 0.1 m is spinning about an axle perpendicular to the disk and running through its center.
a) How many revolutions per second would it have to rotate in order that the acceleration of the outer edge of the disk be 14 g's (i.e., 14 times the gravitational acceleration g)?

b) For the frequency determined in part (a), what is the speed of a point half way between the axis of rotation and the edge of the disk?

c) At this same frequency, what is the period of rotation of this "halfway point"?

d) How long does it take a point on the edge of the disk to travel 1 km?

I got questions a) which is 8.3 seconds.
I am stuck on b). I tried v=$$\omega$$R. I also converted 8.3rev/s back to rpm which was 498rpm. So v=498rpm(.025m)=12.45meters/min. My answer needs to be in m/s so I divided by 60 and got .2075. It's not right. What am I doing wrong?

 

[rgalvan2]

Never mind I got it! :)

 

[baba89]

Hello, it seems like you are on the right track with your calculations. However, there might be a small mistake in your conversion from rpm to m/s. Instead of dividing by 60, you should be dividing by 60 seconds to get the speed in meters per second. So the correct calculation would be 498 rpm x (0.025 m) x (1 min / 60 seconds) = 0.2075 m/s.

I would recommend double-checking your unit conversions and making sure to include the conversion from minutes to seconds in your calculations. Also, make sure to use the correct value for the radius (0.05 m) when solving for the speed at the halfway point.

For part c), you can use the formula T = 1/f where T is the period and f is the frequency (8.3 Hz). And for part d), you can use the formula v = d/t where v is the speed (which you have already calculated) and d is the distance (1 km). I hope this helps! Good luck with your assignment.