In the figure, a thin uniform rod (mass 3.5 kg, length 3.4 m) rotates freely about a horizontal axis A that is perpendicular to the rod and passes through a point at a distance d = 0.77 m from the end of the rod. The kinetic energy of the rod as it passes through the vertical position is 22 J. (a) What is the rotational inertia of the rod about axis A? (b) What is the (linear) speed of the end B of the rod as the rod passes through the vertical position? (c) At what angle will the rod momentarily stop in its upward swing? (a) Number i Units (b) Number i Units (c) Number Units B

A ball of mass M = 1.30 kg and radius r = 4.50 cm is attached to one end of a thin, cylindrical rod of length L = 14.0 cm and mass m = 0.880 kg. The ball and rod, initially at rest in a vertical position and free to rotate around the axis shown in the figure below, are nudged into motion. L m M (a) What is the rotational kinetic energy of the system when the ball and rod reach a horizontal position? J (b) What is the angular speed of the ball and rod when they reach a horizontal position? rad/s V(c) Vfreefall (c) What is the linear speed of the center of mass of the ball when the ball and rod reach a horizontal position? m/s (d) What is the ratio of the speed found in part (c) to the speed of a ball that falls freely through the same distance?

A 2.00-m long rod is hinged at one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. (a) What is the angular acceleration as it is released? (b) What is the angular acceleration when it reaches the vertical position? (c) Which position has the maximum angular velocity (vertical or horizontal)? (d) Which position has the maximum angular acceleration (vertical or horizontal)? (The moment of inertia of a rod about one end is ML2/3.)

A wheel consists of a rim (ring) with a mass of 1.3kg and a radius of 0.45m and four equally-spaced spokes (rods) that run from the center of the wheel to the edge of the rim. Each spoke has a mass of 0.15kg and a length equal to the radius of the wheel. What is the total rotational inertia of the wheel about its center?

Two wheels A and B in the figure are connected by a belt that does not slip. The radius of B is 4.30 times the radius of A. What would be the ratio of the rotational inertias IA/IB if the two wheels had (a) the same angular momentum and (b) the same rotational kinetic energy? (the absolute tolerance for the answer of a is ± 0.001)(the absolute tolerance for the answer of b is ± 0.0001)

In the figure, two particles, each with mass m = 0.88 kg, are fastened to each other, and to a rotation axis at 0, by two thin rods, each with length d = 5.6 cm and mass M = 1.3 kg. The combination rotates around the rotation axis with angular speed w = 0.28 rad/s. Measured about O, what is the combination's (a) rotational inertia and (b) kinetic energy? M. M. Rotation axis (a) Number i Units (b) Number i Units

The figure shows three 0.0114 kg particles that have been glued to a rod of length L= 5.70 cm and negligible mass. The assembly can rotate around a perpendicular axis through point O at the left end. If we remove one particle (that is, 33% of the mass), by what percentage does the rotational inertia of the assembly around the rotation axis decrease when that removed particle is (a) the innermost one and (b) the outermost one? Axis m m (a) Number i Units (b) Number i Units >