P3230. Winter 2001. Asssignment 1. Due February 5.

1. The linear density of a thin rod is given by r = cx² where c is a constant and x is the distance measured from one end. If the rod is of length b, (a) find the center of mass, (b) find the moment of inertia about the CM, (c) find the moment of inertia about the axis passing through the edge (x = 0) of the rod.

2. Find the period of a physical pendulum for which the distance between the point of suspension and the center of oscillation is d.

3. A uniform solid ball has a few turns of light string wound around it . If the end of the string is pulled upwards with the acceleration 0.5g and the ball is allowed to fall under gravity, what is the acceleration of the center of the ball?

4. A billiard ball of radius a is initially spinning about a horizontal axis with angular speed w₀ and with zero forward speed. If the coefficient of sliding friction between the ball and the table is m_k, find the distance the ball travels before slipping ceases to occur.

5. A thin uniform plank of length l lies at rest on a horizontal sheet of ice. If the plank is given a kick at one end in a direction normal to the plank, show that the plank will begin to rotate about a point located a distance l/6 from the center.

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On 24 Jan 2001, 10:33.