3. Consider a father pushing a child on a playground merry-go-round. The system has a moment of inertia of 84.4 kg m². The father exerts a force on the merry-go-round perpendicular to its radius to achieve an angular acceleration of 4.44 rad/s².(a)How long (in s) does it take the father to give the merry-go-round an angular velocity of 2.23 rad/s? (Assume the merry-go-round is initially at rest.) s(b)How many revolutions must he go through to generate this velocity? revolutions(c)If he exerts a slowing force of 270 N at a radius of 1.45 m, how long (in s) would it take him to stop them?

4.(a)Calculate the angular momentum (in kg m²/s) of Neptune in its orbit around the Sun. (The mass of Neptune is 1.020 10²⁶ kg, the orbital radius is 4.497 10⁹ km and the orbital period is 165 y.) kg m²/s(b)Compare this angular momentum with the angular momentum of Neptune on its axis. (The radius of Neptune is 2.476 10⁴ km and the rotation period is 16.11 h.)

L_orbital

L_rotation