ScholarshipMechanicsFree

Despinning the CubeSat Carrier

Rotational dynamics

After separation from a Rocket Lab launcher, a spin-stabilised satellite is spinning about its symmetry axis at

\omega_0 = 3.00\ \text{rad s}^{-1}

. Its body is modelled as a uniform solid cylinder of mass

M = 120\ \text{kg}

and radius

R = 0.500\ \text{m}

, spinning about its axis. Two small masses, each

m = 2.50\ \text{kg}

and treated as point masses, sit on opposite sides of the rim at

r_1 = 0.500\ \text{m}

from the axis. A motor slowly extends two light telescopic booms so that each mass moves radially outward to

r_2 = 2.00\ \text{m}

from the axis, taking

20.0\ \text{s}

. No external torques act on the satellite. The diagram shows the satellite, viewed along its spin axis, before and after the booms extend.

(a)

explain1 mark

State which of the following stay constant as the booms extend: the angular momentum of the satellite system, its rotational kinetic energy, its angular velocity. Justify your answer.

(b)

show that2 marks

Show that the final angular velocity is

\omega_2 = \omega_0\dfrac{\tfrac{1}{2}MR^2 + 2mr_1^2}{\tfrac{1}{2}MR^2 + 2mr_2^2}

, and calculate its value.

(c)

calculate3 marks

Calculate the change in rotational kinetic energy, and hence the average power that the motor must absorb during the extension. Explain, by considering the forces on each mass, why the motor absorbs energy rather than supplies it.

(d)

discuss2 marks

Mission control wants to reduce the spin to 10% of

\omega_0

using longer booms. Calculate the boom radius

r

needed, and discuss whether this method can ever bring the satellite exactly to rest. Discuss whether releasing the masses completely (cutting them free at the end of the booms) could change this conclusion.

Your score: 0 / 8(0 of 4 parts marked — open “Mark it” on each part)