A large wooden turntable in the shape of a flat uniform disk has a radius of 2.0

Question

A large wooden turntable in the shape of a flat uniform disk has a radius of 2.00 m and a total mass of 130 kg . The turntable is initially rotating at 3.00 rad/s about a vertical axis through its center. Suddenly, a 80.0-kg parachutist makes a soft landing on the turntable at a point near the outer edge. a)Find the angular speed of the turntable after the parachutist lands. (Assume that you can treat the parachutist as a particle.) b)Compute the kinetic energy of the system before the parachutist lands. c)Compute the kinetic energy of the system after the parachutist lands.

Explanation / Answer

a)

M = mass of disk = 130 kg

R = radius = 2 m

Id = moment of inertia of table = (0.5) M R2 = (0.5) (130) (2)2 = 260

Wi = initial angular speed = 3 rad/s

I' = moment of inertia of parachutist after landing = mR2 = 80 (2)2 = 320

Wf = final angular speed after landing

a)

Using conservation of angular momentum

Id Wi = (Id + I') Wf

260 (3) = (260 + 320) Wf

Wf = 1.345 rad/s

b)

initial KE = (0.5) Id Wi2 = (0.5) 260 (3)2 = 1170 J

c)

Final KE = (0.5) (Id + I')Wf2 = (0.5) (260 + 320) (1.345)2 = 524.62 J

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.