A person with mass m p = 71 kg stands on a spinning platform disk with a radius

Question

A person with mass mp = 71 kg stands on a spinning platform disk with a radius of R = 2.25 m and mass md = 189 kg. The disk is initially spinning at ? = 1.5 rad/s. The person then walks 2/3 of the way toward the center of the disk (ending 0.75 m from the center).

1)What is the total moment of inertia of the system about the center of the disk when the person stands on the rim of the disk?   kg-m2

2)What is the total moment of inertia of the system about the center of the disk when the person stands at the final location 2/3 of the way toward the center of the disk?   kg-m2

3)What is the final angular velocity of the disk? rad/s

4)What is the change in the total kinetic energy of the person and disk? (A positive value means the energy increased.) J

5)What is the centripetal acceleration of the person when she is at R/3? m/s2

6)If the person now walks back to the rim of the disk, what is the final angular speed of the disk? rad/s

A person with mass mp = 71 kg stands on a spinning platform disk with a radius of R = 2.25 m and mass md = 189 kg. The disk is initially spinning at ? = 1.5 rad/s. The person then walks 2/3 of the way toward the center of the disk (ending 0.75 m from the center). 1)What is the total moment of inertia of the system about the center of the disk when the person stands on the rim of the disk? kg-m2 2)What is the total moment of inertia of the system about the center of the disk when the person stands at the final location 2/3 of the way toward the center of the disk? kg-m2 3)What is the final angular velocity of the disk? rad/s 4)What is the change in the total kinetic energy of the person and disk? (A positive value means the energy increased.) J 5)What is the centripetal acceleration of the person when she is at R/3? m/s2 6)If the person now walks back to the rim of the disk, what is the final angular speed of the disk? rad/s

Explanation / Answer

1) I1 = Idisk + Iperson = 0.5*md*R^2 + mp*R^2

I1 = (0.5*189*2.25*2.25) + ( 71*2.25*2.25) = 837.84375 kg m^2

2) I2 = Idisk + Iperson = 0.5*md*R^2 + mp*(2/3)R^2

I1 = (0.5*189*2.25*2.25) + ( 71*0.75*0.75) = 518.34375 kg m^2

3) L2 = L1

I1*w1 = I2*w2

w2 = (I1*w1)/I2 = 2.42 rad/s

4) K2 - K1 = 0.5*I2*w2^2 - 0.5*I1*W1^2 =(0.5*518.34375 *2.42*2.42)-(0.5*837.84375*1.5*1.5) = 575.23995 J

5) a = (R/3)*w2^2 = 4.3923 m/s^2

6) w = 1.5 rad/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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