Merry go round Rotation Problem

[KTiaam]

Homework Statement

A merry - go - round rotates clockwise 15 times in 45 seconds. By rubbing against its edge, a child stop it from turning in 15 seconds.

a) find its initial angular velocity (ω)
b) find its angular acceleration ([itex]\alpha[/itex])

The Attempt at a Solution

15 times in 45 seconds means:

in 1 second it makes 1/3 of a revolution

thus in 3 seconds it make on complete revolution

im not sure if I am going in the right direction but Angular Velocity is in radians per second.

Am i on the right track? Do i just take the reciprocal of my answer? Please help

 

[TSny]

You found that it makes 1/3 revolution per second. Can you convert 1/3 revolution to radians?

 

[KTiaam]

You found that it makes 1/3 revolution per second. Can you convert 1/3 revolution to radians?

2/3 pi radians?

 

[TSny]

Yes.

 

[Nickie]

I would suggest approaching this problem using the equation for angular velocity, which is ω = Δθ/Δt, where ω is the angular velocity in radians per second, Δθ is the change in angle in radians, and Δt is the change in time in seconds. In this case, we know that in 45 seconds, the merry-go-round rotates 15 times, which means it rotates 15*2π = 30π radians. Therefore, the initial angular velocity can be calculated as:

ω = (30π radians)/(45 seconds) = 2π/3 radians per second

For the second part of the problem, we can use the equation for angular acceleration, which is α = Δω/Δt, where α is the angular acceleration in radians per second squared and Δω is the change in angular velocity in radians per second. In this case, we know that the child stops the merry-go-round from rotating in 15 seconds, which means that the final angular velocity is 0 radians per second. Therefore, the angular acceleration can be calculated as:

α = (0 radians per second - 2π/3 radians per second)/(15 seconds) = -2π/45 radians per second squared

This negative value indicates that the merry-go-round is decelerating. I hope this helps!