How Do You Solve Complex Physics Problems Involving Rotational Motion?

[thebigeis]

Impossible Physx Homework!

I have a few problems left that I'm completely stumped on how to do.

#1) A typical lab centrifuge rotates at 4000rpm. Test tubes have to be placed into a centrifugre very carefully because of the very large aceelerations. What is the acceleration at the end of a test tube that is 10cm from the axis of rotation in?

#2) A 5m-diameter merry-go-round is initially turning with a 4s period. It slow down and stops in 20s. Before slowing what is the speed of a child on the rim? How many revs does the merry-go-round make as it stops?

Out of my 6, these trouble me the most. For #1, I made the radius 10cm, the velocity constant, but am unsure what equations I need to plug those in. As for #2, it's thet same deal. In one, I have the period, and in the other I'm left with the velocity, and with both I have the radius, but have no idea where to put them. Please, help with a point in the right direction.

 

[grant9076]

The accelleration is equal to the tangential velocity squared divided by the radius (v^2/r). If you multiply the radius (.1m) by 2*Pi, you will get the distance traveled in one revolution. You then multiply this distance by 4000 rpm to get the velocity in meters/minute and divide by 60 to get the velocity in meters per second. Since you now have the radius, and the velocity, you can now square the velocity and divide by the radius to get the accelleration. I can tell you right away that the accelleration is going to be very high.

 

[kyle8921]

It sounds like you are struggling with some basic concepts in kinematics and rotational motion. For question #1, you will need to use the equation for centripetal acceleration, which is given by a = v^2/r, where v is the velocity and r is the radius. Since the velocity is constant, you can use the given speed of 4000rpm to solve for the velocity and then plug that into the equation. Remember to convert the rpm to radians per second before solving.

For question #2, you will need to use the equation for angular velocity, which is given by ω = 2π/T, where T is the period. You can use this equation to find the initial angular velocity of the merry-go-round, and then use that to find the initial linear velocity of the child on the rim. To find the number of revolutions the merry-go-round makes as it slows down, you will need to use the equation ω = ω0 + αt, where α is the angular acceleration and t is the time. You can use this equation to find the angular acceleration, and then use that to find the final angular velocity. From there, you can find the number of revolutions by dividing the final angular velocity by the initial angular velocity.

I hope this helps point you in the right direction. Remember to always start with the relevant equations and plug in the given values, and don't forget to convert units when necessary. If you are still struggling, I recommend seeking help from a classmate, teacher, or tutor. Good luck!