Question

10*) The Sun has approximate radius 7×108 m, and rotates around its axis once every 27 days. a) Find its angular velocity in rad/s, and (assuming it is a uniform sphere) write a formula for its angular momentum expressing it in terms of its mass M (you do not need to substitute a value for M). b) Suppose the Sun were to collapse to a neutron star, which is a much denser state, without losing any mass and without being affected by external torques. If the Sun becomes a neutron star of radius 7 × 104 m, what would be its angular velocity? How many revolutions per second would it be doing? (The mass of the Sun cancels out of the angular momentum conservation equation).Your result should be between 10 and 100 revolutions per second, a much faster rotation than the initial one. Angular momentum conservation thus predicts the existence of fast-rotating neutron stars, also known as pulsars. Use the Moment of Inertia Of Objects with uniform density Table attached.

TABLE 12.2 Moments of inertia of objects with uniform density Object and axis Picture Object and axis Picture Thin rod, about center 1 ML Cylinder or disk, about center \MR Thin rod, about end ŽML Cylindrical hoop, about center MR2 Plane or slab, about center 12 Ma2 Solid sphere, about diameter MR Plane or slab, about edge Ma? Spherical shell, about diameter ŽMR2

Answer 1

a) Th angular velocity is: w1 = T Where T is the period: T = 27 days = 27 * 24 * 60 * 60 = 2332800 s 21 W. = 2332800 = 2.69 x 10-6 rad The angular moment is giving by: 1x = 1w = (MR2) b) Using the conservation of angular momentum: L = L2 (MR2) as = (& mra) az Solving for wz we = wa ( Using the giving values: w = (2.69 x 10-6) (7:10)* w2 = 2697ad The number of revolutions per second is: