🚀 go-pugleaf

Could someone help me with some physics problems please i would really
appreciate it.

1)  a child hunting for his favorite wooden horse, is running on the ground
around trhe edge of a stationary merry-go-round.  the angular speed of the
child has a constant value of 0.250 rad/s.  at the instant the child spots
the horse, one-quarter of a turn away, the merry-go-round began to move (in
the direction of the child running) with a constant angular acceleration of
0.0100 rad/s^2.  what is the shortest time it takes for the child to catch up
to the horse?

2)a solid ball of mass M and radius R starts at rest at height h above the
bottom of a path with a positive parabolic shape.  it rolls without slipping
down the left side of the path.  the right side of the path, starting at the
bottom,  is frictionless.  to what height does the ball rise on the right?

3)  a skater's body has rotational inertia 4.2 (kg)m^2  with his fists held
to his chest and 5.7 kg(m^2) with arms outstreched.  the skater is twirling
at 3.0 rev/s while holding 2.5 kg weights in each outstretched hand; the
weights are 76 cm from his rotation axis.  if he pulls his hands in to his
chest how fast wil he be twirling?

4)  a physics student is standing on an initially motionless, frictionless
turntable with rotational inertia 0.31 kgm^2.  he's holding a wheel of
rotational inertia 0.22 kgm^2 spinning at 130 rpm about a vertical axis. 
when he turns the wheel upside down, student and turntable begin rotating at
70 rpm.  a) what is the students' mass, considering him to be a cylinder 30
cm in diameter?  b)  how much work did he do in turning the wheel upside
down?  neglect the distance between the axes of the turntable and wheel.

thanks