Question

A rotor disk in your car's wheel with radius of 30.0 cm and mass of 15.0 kg rotates with 800 rpm and it slows down to 50 rpm in 10 second. Find its angular acceleration? (b) Number of revolutions during this period of time (c) The required force to do this action during this period of time. Antares is a star in Scorpius constellation. Its radius is 3.0AU and its mas is about 12 times the mass of the sun. Antares orbital speed is 20.7 km/sec. Eventually after a couple million years Antares will be converted to a neutron star. ts radius will be 4.3*10-5 AU. Find its orbital speed after it becomes neutron star? Find your answer by rpm. Moment of inertia of sphere is I= 2/5 MR2

Answer 1

1. Moment of inertia of the wheel, I = 1/2 mr²

I = (0.5*15*0.3²) kgm²

= 0.675 kgm²

Initial angular speed, w_o = 800 rpm = (800*$\pi$/30) rad/s

= 83.74 rad/s

Final angular speed, w = 50 rpm = (50*$\pi$/30) rad/s

= 5.24 rad/s

Time, t = 10 sec, so, using, w = w_o+$\alpha$t, we have,

5.24 = 83.74 + $\alpha$ *10

Or, $\alpha$ = (5.24-83.74)/10

= - 7.85

(a) Angular acceleration = - 7.85 rad/s²

(b) Again using, w² - w_o² = 2$\alpha$$\theta$, we have,

5.24² - 83.74² = -2*7.85*$\theta$

Or,   $\theta$ = 444.9

So, number of revolutions = (444.9*30/3.14) = 4250.64

(c) Torque acting on the wheel = I$\alpha$ = -(0.675*7.85) Nm

= - 5.298 Nm

Negative sign shows the torque causes retardation.

Now, Torque = Force*Radius

Or,    5.298 = Force*0.3

Or,    Force = (5.298/0.3) N

= 17.66 N