Lily is a 50 kg diver. At the instant of takeoff, her angular momentum about her

Question

Lily is a 50 kg diver. At the instant of takeoff, her angular momentum about her transverse axis is 20 kg x m^2/s. Her radius of gyration about the transverse axis is 0.4 m at this instant. During the dive, Lily tucks and reduces her radius of gyration about the transverse axis to 0.2 m.

A. At takeoff, what is Lily's moment of inertia about her transverse axis?

B. At takeoff, what it Lily's angular velocity about the transverse axis?

C. After Lily tucks, what is her moment of inertia about her transverse axis?

D. After Lily tucks, what is her angular velocity about the transerse axis?

Answers:

A. 8.0 kg x m^2

B. 2.5 rad/s

C. 2.0 kg x m^2

D. 10.0 rad/s

Explanation / Answer

A.

I = m Rg^2

where Rg = the radius of gyration. Thus, initially, Rg = 0.4 m,

I = 50 kg (0.4 m)^2 = 8.0 kg m^2 [ANSWER]

************

B.

As

L = I w --> w = L / I

Then

w = (20 kg m^2/s) / (8 kg m^2)

w = 2.5 rad/s [ANSWER]

************

C.

If = m Rgf^2

As Rgf = 0.2 m,

If = 2.0 kg m^2 [ANSWER]

***************
D.

The angular momentum is still at 20 kg m^2/s by conservation of angular momentum.

Thus,

w = L / If = 10 rad/s [ANSWER]

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