Question

A playground carousel is rotating counterclockwise about its center on frictionless bearings. A person standing still on the ground grabs onto one of the bars on the carousel very close to its outer edge and climbs aboard. Thus, this person begins with an angular speed of zero and ends up with a nonzero angular speed, which means that he underwent a counterclockwise angular acceleration. The carousel has a radius of 1.62 m, an initial angular speed of 3.35 rad/s, and a moment of inertia of 126 kg·m2. The mass of the person is 41.1 kg. Find the final angular speed of the carousel after the person climbs aboard.

Answer 1

the final angular speed of the carousel after the person climbs aboard is 1.8 rad/s

Step-by-step explanation:

given information:

R = 1.62 m

ω0 = 3.35 rad/s

I0 = 126 kg/
`m^(2)`

m = 41.1 kg

final angular speed

total of momen inertia

I = I0+ m
`R^(2)`

= 126 + (41.1)(
`(1.62^(2))`

= 126 + 107.86

= 233.86

I ω = I0 ω0

ω = I0 ω0 / I

= (126)(3.35)/233.86

= 1.8 rad/s