# Magnitude of Acceleration on Merry-Go-Round

• teresalin2004
In summary, the question asks for the magnitude of acceleration of a 30 kg child on a 2.1 meter diameter merry-go-round that is pushed from rest to a final speed of 1.7 rotations per second in 25 seconds. Using radians, the angular acceleration is found to be 0.427 rad/s². However, the attempt at solving the question using rω² is incorrect as the diameter must be converted to radius and there is only one question to be answered.
teresalin2004

## Homework Statement

At a playground you let your kid sister (30 kg) kneel on the surface (near the edge) of a 2.1 meter diameter merry-go-round. You push the merry-go-round so that it constantly accelerates from rest to a final speed of 1.7 rotations per second at the end of a 25 second interval. (please complete all questions using radians)
After it comes up to speed, you stop pushing and the merry-go-round continues to run at a constant rate of 1.7 rotations per second. What is the magnitude of your sister's acceleration, if any?

## Homework Equations

V is the tangental velocity in m/s
r is radius of circle in meters
ω is angular velocity in radians/sec
a is in m/s²
[/B]
ang. acc. = Δω/Δt = 10.68/25 = 0.427 rad/s²

## The Attempt at a Solution

I got the first part of the question right, but I have no idea what I am doing wrong for the last part shown above. This is what I did:

a = rω² = (2.1)(10.68)² = 240 m/s²
[/B]

in the first place, 2.1 meters is the diameter, and you have to use the radius. In the second place, as far as I can see there is only one question.

## What is the definition of acceleration in relation to a merry-go-round?

Acceleration is the rate of change of velocity over time. In the context of a merry-go-round, it refers to the change in speed or direction of the riders as the ride rotates.

## How does the speed of a merry-go-round affect the acceleration experienced by the riders?

The speed of a merry-go-round directly affects the acceleration experienced by the riders. The faster the ride spins, the greater the acceleration felt by the riders due to the change in velocity.

## What factors contribute to the acceleration experienced on a merry-go-round?

The main factor contributing to acceleration on a merry-go-round is the rotation of the ride. Other factors such as the weight and position of the riders can also affect the acceleration experienced.

## Is there a difference in acceleration between the outer and inner parts of a merry-go-round?

Yes, there is a difference in acceleration between the outer and inner parts of a merry-go-round. The outer part, which has a larger radius, has a greater linear speed and therefore experiences a greater acceleration compared to the inner part.

## How can acceleration on a merry-go-round be calculated?

To calculate acceleration on a merry-go-round, the linear speed and angular velocity of the ride must be known. The formula for acceleration is a = rω^2, where a is acceleration, r is the radius of the ride, and ω is the angular velocity.

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