Question

A child sits on a merry‑go‑round that has a diameter of 4.00 m. The child uses her legs to push the merry‑go‑round, making it go from rest to an angular speed of 17.0 rpm in a time of 35.0 s.

What is the average angular acceleration αavg of the merry‑go‑round in units of radians per second squared (rad/s2)?

αavg: _______rad/s^2

What is the angular displacement Δθ of the merry‑go‑round, in units of radians (rad), during the time the child pushes the merry‑go‑round?

Δθ: _______ radians

What is the maximum tangential speed vmax of the child if she rides on the edge of the platform?

vmax:________m/s

Answer 1

here,

the diameter , d = 4 m

the initial angular speed , w0 = 17 rpm = 1.78 rad/s

time taken , t = 35 s

a)

let the average angular acceleration of the merry‑go‑round be alpha

using first equation of motion

w = w0 + alpha * t

1.78 = 0 + alpha * 35

alpha = 5.083 * 10^-2 rad/s^2

b)

the angular displacement theta of the merry‑go‑round, theta = w^2 /2*alpha

theta = 1.78^2 /(2*5.083 * 10^-2) rad

theta = 31.2 rad

c)

the maximum tangential speed vmax of the child if she rides on the edge of the platform,v = r * w

v = 4 * 1.78 m/s = 7.12 m/s