Torque and Moment of Inertia

1. Can an object rotate if there is not torque acting?
2. Can a given object have more than one moment of inertia?
3. Does an applied net torque always increase the angular speed of an object?
4. If the angular velocity of an object is zero at some instant, does this mean that the net torque on the object must be zero?
5. Four particles of mass m are connected by massless rods to form a rectangle of sides 2a and 2b as shown below. The system rotates about an axis in the plane of the figure through the center. Find the moment of inertia about this axis.

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7. Using same information as previous problem, find the moment of inertia if the axis of rotation where through two of the masses.
8. A string is wound around the rim of a uniform disk that is pivoted to rotate without friction about a fixed axis through its center. The mass of the disk is 3kg, and its radius is 25cm. The string pulled with a force F of magnitude 10 N. If the disk is initially at rest, what is its angular velocity after 5s?

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10. An object of mass m is tied to a light string wound around a wheel of moment of inertia I and radius R.(below). The wheel bearing is frictionless, and the string does not slip on the rim. Find the tension in the string and the acceleration of the object. (This problem is to be completed analytically, no calculus is needed.)