Circular Motion (standing on a carousel)

[dragonladies1]

Hi again,

I'm sorry for all of the questions in this section. I am having the worst time trying to understand how to set up the problems. I know the equation for acceleration is a= V^2/r; however for this problem I am looking to find the velocity and time. Again, I would appreciate any kind of help possible.

What are the period and speed of a person on a carousel if the person has an acceleration with a magnitude of 0.7 m/s2 when she is standing 3.8 m from the axis?

What are her acceleration magnitude and speed if she then moves to a distance of 2.1 m from the carousel center and the carousel keeps rotating with the same period?

Thank you!

 

[tiny-tim]

Hi dragonladies1!

(try using the X² tag just above the Reply box )

Just apply your v²/r formula (and use v = ωr).

 

[dragonladies1]

Thank you. Using my v2/r formula I came up with 55.63 and I"m not sure what the other formula is. My teacher hasn't mentioned anything using omega.

 

[tiny-tim]

oh, it's just the fairly obvious formula that if your radius is r cm, and your angular speed is ω radians per second, then your actual speed (tangential) is ωr cm per second.

(and the period is 2π/ω seconds)

 

[dragonladies1]

Ok, so I determined that the speed is 1.63, but I don't know why I can't figure out how to find the period for my problem. I plugged in

Period= 2π/.43=14.65.

Is this correct?

 

[tiny-tim]

Ok, so I determined that the speed is 1.63, but I don't know why I can't figure out how to find the period for my problem. I plugged in

Period= 2π/.43=14.65.

Is this correct?

Yup!

(or 14.64)

(The reason why it's 2π/(angular speed) is because the period T is the time it takes to go 2π: so (angular) speed = (angular) distance over time, so ω = 2π/T. wink:)