1. Three objects are situated at different positions on the x-axis. The first object has a mass of 7.1 kg and is at x= 4.4 m, the second has a mass of 2.4 kg and is at x= 5.3 m, and the third has a mass of 1.6 kg. The axis of rotation passes through the origin perpendicular to the x-axis. What is the magnitude of the distance between the third mass and the origin if the moment of inertia (or the rotational inertia) of the system is 951.0 kg m2?

2. A large 64.1 kg pottery wheel has a radius of 0.71 m, and can be considered as a solid cylinder rotating about an axis through its centre. How much work must be done on the pottery wheel to increase the rate at which it is spinning from 90.0 rpm (rotations per minute) to 124.0 rpm? Give your answer in J.

Hint: The moment of inertia for a solid cylinder rotating about its centre with mass M and radius R is given by: I = 1/2 MR2.

3. A person exerts a force of 49.9 N on the end of a door which is 80.7 cm wide (i.e. they exert the force a distance of 80.7 cm from the pivot point of the door hinges). What is the magnitude of the torque if the force is exerted perpendicular to the door? Express your answer in units of N m.