What are the formulas for finding angular and linear speed on a merry-go-round?

[eagles12]

Homework Statement

Two children ride on the merry-go-round. Child 1 is 2.0m from the axis of rotation, and child 2 is 1.5m from the axis. If the merry go round completes one revolution every 4.1s, find the angular speed and the linear speed of each child.

Homework Equations

w=Δθ/Δt
T=2∏/w

The Attempt at a Solution

a=v^2/r
a=v^2/2

a=v^2/1.5

 

[tiny-tim]

hi eagles12!

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

Two children ride on the merry-go-round. Child 1 is 2.0m from the axis of rotation, and child 2 is 1.5m from the axis. If the merry go round completes one revolution every 4.1s, find the angular speed and the linear speed of each child.
…
a=v^2/r

yes, that's the acceleration …

but the question asks only for ω and v ​

 

[eagles12]

im a little confused on how to find θ

 

[tiny-tim]

… If the merry go round completes one revolution every 4.1s …

so θ = one revolution = 2π

 

[eagles12]

so I do w=2π/(1/4.1) and I got 25.76 but that is incorrect

 

[eagles12]

is the angular speed for each kid the same? I am not sure how the mass factors in, or is that just factored into the linear velocity?

 

[tiny-tim]

hi eagles12!

(just got up :zzz:)

so I do w=2π/(1/4.1) and I got 25.76 but that is incorrect

ω is (angular) speed, so it's (angular) distance over time …

in this case 2π/4.1 ​

is the angular speed for each kid the same? I am not sure how the mass factors in, or is that just factored into the linear velocity?

yes ω is the same for the whole of a rigid body, and for anything attached to it (like the kids)

mass is irrelevant, mass is physics …

finding the angular or linear velocity from the time and angle etc is just geometry (maths) …

you won't need the mass until you start finding the force