In a double-star system, two stars of mass 4.9 x 1030 kg each rotate about the system's center of mass at radius 1.2 x 1011 m. (a) What is their common angular speed? (b) If a meteoroid passes through the system's center of mass perpendicular to their orbital plane, what minimum speed must it have at the center of mass if it is to escape to "infinity" from the two-star system? (a) Number Units (b) Number Units

a) Calculate the angular momentum (in kg · m2/s) of Mercury in its orbit around the Sun. (The mass of Mercury is 3.300 ✕ 1023 kg, the orbital radius is 5.790 ✕ 107 km and the orbital period is 0.241 y.)  kg · m2/s (b) Compare this angular momentum with the angular momentum of Mercury on its axis. (The radius of Mercury is 2.440 ✕ 103 km and the rotation period is 1408 h.) Lorbital Lrotation  =

A mountain biker takes a jump in a race and goes airborne. The mountain bike is traveling at 12.5 m/s before it goes airborne. If the mass of the front wheel on the bike is 950 g and has radius 30 cm, what is the angular momentum (in kg · m/s) of the spinning wheel about its axis in the air the moment the bike leaves the ground? (Assume the wheel can be approximated by a hoop rotating about its center of mass that rolls without slipping before the jump. Enter the magnitude.) kg · m2/s

A 3.0-kg mass slides on a frictionless horizontal surface with a speed of 3.0 m / s when it collides with a 1.0-kg mass initially at rest as shown in the figure. The two masses stick to each other and slide on a frictionless circular wheel portion of radius 0.40 m. At what maximum height h, above the horizontal, do the masses reach? Answers: a) 0.18 m       b) 0.15 m      c) 0.21 m      d) 0.26 m        e) 0.40 m

A cockroach of mass m lies on the rim of a uniform disk of mass 3.00 m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.434 rad/s. Then the cockroach walks halfway to the center of the disk.(a) What then is the angular velocity of the cockroach-disk system?(b) What is the ratio K/K0 of the new kinetic energy of the system to its initial kinetic energy?

A cockroach of mass m lies on the rim of a uniform disk of mass 6.00 m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.502 rad/s. Then the cockroach walks halfway to the center of the disk. (a) What then is the angular velocity of the cockroach-disk system? (b) What is the ratio K/Ko of the new kinetic energy of the system to its initial kinetic energy? (a) w = i (b) K/Ko =

A massless, frictionless merry-go-round of radius R has one child of mass M sitting on the outer edge and is spinning with angular velocity ωi. If the child walks towards the center until she is 0.50R from the center, by what factor does the angular velocity increase? (i.e. solve for F where ωf=Fωi)