A light rod of length ℓ = 1.00 m rotates about an axis perpendicular to its length and passing through its center as in the figure below. Two particles of masses m1 = 4.40 kg and m2 = 3.00 kg are connected to the ends of the rod. (a) Neglecting the mass of the rod, what is the system's kinetic energy when its angular speed is 2.40 rad/s? (b) Repeat the problem, assuming the mass of the rod is taken to be 2.35 kg.

The figure shows three 0.0172 kg particles that have been glued to a rod of length L=6.24 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? (a) Number i (b) Number Axis Units Units |--d- m d m -d m

The figure below is of an overhead view of a thin uniform rod of length 0.730 m and mass M rotating horizontally at angular speed 20.5 rad/s about an axis through its center. A particle of mass M/3.00 attached to one end is ejected from the rod and travels along a path that is perpendicular to the rod at the instant of ejection. If the particle's speed v, is 6.00 m/s greater than the speed of the end of the rod just after ejection, what is the value of vp? m/s Rotation axis

In the figure, two particles, each with mass m = 0.78 kg, are fastened to each other, and to a rotation axis at O, by two thin rods, each with length d = 5.5 cm and mass M = 1.3 kg. The combination rotates around the rotation axis with angular speed ω = 0.32 rad/s. Measured about O, what is the combination's (a) rotational inertia and (b) kinetic energy?

The figure shows three 0.0186 kg particles that have been glued to a rod of length L=5.67 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 (a) Number Units (b) Number Units

In the figure, two particles, each with mass m = 0.84 kg, are fastened to each other, and to a rotation axis at O, by two thin rods, each with length d = 5.6 cm and mass M = 1.0 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? (a) Number 8 M Rotation axis (b) Number i M m Units Units

A disk of mass M is spinning freely at 9.27 rad/s when a second identical disk, initially not spinning, is dropped onto it so that their axes coincide. In a short time the two disks are corotating. HINT (a) What is the angular speed of the new system (in rad/s)? rad/s (b) If a third such disk is dropped on the first two, find the final angular speed of the system (in rad/s). rad/s

An electric turntable 0.750 m in diameter is rotating about a fixed axis with an initial angular velocity of 0.250 rev/s and a constant angular acceleration of 0.900 rev/s2.(a) Compute the angular velocity of the turntable after 0.200 s.(b) Through how many revolutions has the turntable spun in this time interval?(c) What is the tangential speed of a point on the rim of the turntable at t = 0.200 s?(d) What is the magnitude of the resultant acceleration of a point on the rim at t = 0.200 s?

In the figure below, the disk, of mass 440 g and radius 3.5 cm, is rotating at 180 rpm on a frictionless shaft of negligible radius. The upper disk, of mass 270 g and radius 2.3 cm, is initially not rotating. It drops freely down onto the lower dis, and frictional forces bring the two disk to a common rotational speed. Find (a) that common speed and (b) the fraction of the initial kinetic energy lost to friction.

The figure shows three 0.0146 kg particles that have been glued to a rod of length L-5.58 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? (a) Number (b) Number Axis Units Units 0 m m m |a+d+d+