A playground merry-go-round is approximately a solid 150kgsolid disk (Icom=1/2MR

Question

A playground merry-go-round is approximately a solid 150kgsolid disk (Icom=1/2MR^2) of radius 1.5m. A 55kg child sits in aseat at the outer rim of the disk while the merr-go-round isrevolving about a vertical axis at a rate of 1 revolution every 10seconds. The child then stands up and walks to the very center ofthe disk. (OK to pretend child is a point mass first on the rim andthen at the very center). A) What is the rotational inertia (moment of inertia) of thesystem (child and merry-go-round) about the central vertical axisbefore the child stands up to move? B) What was the angular momentum of the system about thevertical axis before the child moved? C) What is the angular speed of the merry-go-round (expressedin either rad/sec or RPM) AFTER the child reaches the center? D) I know that the Mechanical Energy of the system is notconserved during this process, but why? A playground merry-go-round is approximately a solid 150kgsolid disk (Icom=1/2MR^2) of radius 1.5m. A 55kg child sits in aseat at the outer rim of the disk while the merr-go-round isrevolving about a vertical axis at a rate of 1 revolution every 10seconds. The child then stands up and walks to the very center ofthe disk. (OK to pretend child is a point mass first on the rim andthen at the very center). A) What is the rotational inertia (moment of inertia) of thesystem (child and merry-go-round) about the central vertical axisbefore the child stands up to move? B) What was the angular momentum of the system about thevertical axis before the child moved? C) What is the angular speed of the merry-go-round (expressedin either rad/sec or RPM) AFTER the child reaches the center? D) I know that the Mechanical Energy of the system is notconserved during this process, but why?

Explanation / Answer

I0 = 1/2 (M + m) R2   theinitial moment of inertia of merry-go-round + child Angular Momentum = I0 0 = 2 f I = 2 I / 10     where f = 1 sec /10 I = M R2    when the child reachesthe center I = I0 0 = (M + m) 0 /M       angular speed when childreaches the center The child did work on the merry-go-round when walking towardsthe center which was responsible for the increase in angular speed Angular momentum is proportional to andKinetic energy is proportional to 2 = (M + m) 0 /M       angular speed when childreaches the center The child did work on the merry-go-round when walking towardsthe center which was responsible for the increase in angular speed Angular momentum is proportional to andKinetic energy is proportional to 2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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