A student sits on a rotating stool holding two 4.0 kg objects. When his arms are

Question

A student sits on a rotating stool holding two 4.0 kg objects. When his arms are extendedhorizontally, the objects are 1.0 m from the axis of rotation, andhe rotates with an angular speed of 0.75 rad/s. The moment ofinertia of the student plus stool is 3.0 kg·m2and is assumed to be constant. The student then pulls the objectshorizontally to 0.20 m from the rotationaxis.(a) Find the new angular speed of the student.
1 rad/s
(b) Find the kinetic energy of the student before and after theobjects are pulled in. before 2 J after 3 J before 2 J after 3 J

Explanation / Answer

Initial moment of inertia is that of the student & stoolplus the two masses: Ii = 3.0 + 4.0x1.02 + 4.0x1.02 = 11.0 kgm2 Final moment of inertia is same idea, but the masses arecloser: If = 3.0 + 4.0x0.202 + 4.0x0.202 =  3.32 kgm2   Now, since angular momentum is conserved: Ii i =   If f           11.0 x 0.75  =  3.32 x      or   final =  2.48rad/s initial KE = (1/2) I 2= (1/2)  x 11.0 x 0.752 =3.09 J final KE = (1/2) I 2 = (1/2)  x  3.32  x1.932 = 6.18 J Now, since angular momentum is conserved: Ii i =   If f           11.0 x 0.75  =  3.32 x      or   final =  2.48rad/s initial KE = (1/2) I 2= (1/2)  x 11.0 x 0.752 =3.09 J final KE = (1/2) I 2 = (1/2)  x  3.32  x1.932 = 6.18 J Now, since angular momentum is conserved: Ii i =   If f           11.0 x 0.75  =  3.32 x      or   final =  2.48rad/s initial KE = (1/2) I 2= (1/2)  x 11.0 x 0.752 =3.09 J final KE = (1/2) I 2 = (1/2)  x  3.32  x1.932 = 6.18 J

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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