Two children standing on opposite sides of a merry-go-round are trying to rotate it. they each push in opposite directions with forces of magnitude 10.2 n. (a) if the merry-go-round has a mass of 180 kg and a radius of 1.8 m, what is the angular acceleration of the merry-go-round? (assume the merry-go-round is a uniform disk.)

First, we can calculate this in terms of linear acceleration using the formula of Newton’s 2nd law:

F = m a

a = F / m

a = 10.2 N / 180 kg

a = 0.057 m / s^2

The relationship between angular velocity (a) and angular velocity (ω) is:

ω = a / r

ω = (0.057 m / s^2) / 1.8 m

ω = 0.031 rad / s^2

To get an answer in terms of degrees per s^2, we multiply it with the conversion factor = 180˚ / π

ω = (0.031 rad / s^2) (180˚ / π rad)

ω = 1.8˚ / s^2

ANSWER: 0.031 rad / s^2       or          1.8˚ / s^2

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2