Final answer:
The magnitude of the total angular momentum of the woman-plus-disk system is calculated by summing the individual angular momenta of the woman and the disk. It amounts to 1680 kg · m2 × π rad/s.
Step-by-step explanation:
To calculate the magnitude of the total angular momentum of the woman-plus-disk system, we need to consider both the woman and the disk as separate parts and then sum their angular momenta. The angular momentum (L) of a rotating object can be calculated using the formula L = I ω, where 'I' is the moment of inertia and 'ω' is the angular velocity in radians per second.
First, we convert the angular velocity from revolutions per second to radians per second by multiplying with 2π (since one revolution is 2π radians):
ω (woman + disk) = 0.50 rev/s × 2π rad/rev = π rad/s
The moment of inertia for the disk (Idisk) can be calculated using the formula Idisk = (1/2)MR2, where M is the mass of the disk and R is its radius.
Idisk = (1/2)(110 kg)(4.0 m)2 = 880 kg · m2
The angular momentum of the disk (Ldisk) is then:
Ldisk = Idisk ω = 880 kg · m2 × π rad/s
Regarding the woman, since she is standing on the rim of the disk, we treat her as a point mass, so her moment of inertia is Iwoman = mr2 where m is her mass and r is her distance from the axis of rotation (the radius of the disk).
Iwoman = (50 kg)(4.0 m)2 = 800 kg · m2
The angular momentum of the woman (Lwoman) is:
Lwoman = Iwoman ω = 800 kg · m2 × π rad/s
The total angular momentum of the woman-plus-disk system (Ltotal) is the sum of their individual angular momenta.
Ltotal = Lwoman + Ldisk
Ltotal = (800 kg · m2 + 880 kg · m2) × π rad/s = 1680 kg · m2 × π rad/s
Therefore, the total angular momentum of the system is 1680 kg · m2 × π rad/s.