Torque, rotation and static equilibrium

Use this for “A 300 N child sits 2 m from the pivot. Where must a 400 N child sit to balance, and how hard does the pivot push up?”

Use this for “A wheel of radius 0.4 m turns through 135°. What is that angle in radians, and how far does a point on its rim travel?”

Use this for “A wheel of radius 0.30 m turns at 120 rpm. What is its angular speed in rad/s, and how fast does its rim move?”

Use this for “A fan turning at 3 rad/s speeds up at 2 rad/s² for 4 s. How fast is it turning, and how many turns does it make?”

Use this for “A 3 N·m torque turns a 2 kg disk of radius 0.5 m. What is its angular acceleration? What if it were a hoop?”