A21-kg child starts at the center of a playground merry-go-round that has a radius of 1.7 m and rotational inertia of 500 kg⋅m2 and walks out to the edge. the merry-go-round has a rotational speed of 0.20 s−1 when she is at the center. what is its rotational speed when she gets to the edge?

Explanation:

given,  

radius of merry - go - round = 1.7 m  

mass of children = 21 Kg

rotational inertia of merry go round = 500 Kg.m²

rotational speed = 0.2 s⁻¹

I₁ = 500 Kg.m²

I₂ = I₁ + m R²

I₂ = 500 + 21 x 1.7²

I₂ = 560.69 Kg.m²

using equation

  I₁ ω₁ = I₂ ω₂

 500 x 0.2  = 560.69 ω₂

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s

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