Question

A student sits on a rotating stool holding two 3.2-kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg · m² and is assumed to be constant. The student then pulls in the objects horizontally to 0.23 m from the rotation axis.

a. Find the new angular speed of the student. _____rad/s

b. Find the kinetic energy of the student before and after the objects are pulled in. before___J after___J

Answer 1

3.2kg 3.2kg r 0.23 0.23 M m m Ms sw=0,75 radls Laim new I = Studeny + stool m 2 3kg. Net torque about the axis of rotation is zero therefore angular momentum of student stool and objects system remains conserved. Lsystem, i = Lsystem. f (Astud "student + stoot + lobjects )os = ((student + stod. student + stool + lobject ) ® new (3 +2mR2) = (3+2mr2 )o, new = @new 3+2mR2 0 3+2mr2 new (3) + (2) (3.2)*(1) x (0.75) (3) + (2) (3.2) (0.23)? new -2.112rad/s the new angular speed of the student is 2.112 rad/s the kinetic energy of the student before the objects student are pulled in KE before - 1/2 x (1 stru student + stool + lobjects )co2 KE before = } < (3 + 2mR?)o» KE before = } x {(3) + (2) * (3.2) < (1)2} < (0.75)2

KED = & before 2.644) the kinetic energy of the student after the objects student are pulled in KE after = < < (1stu student + stool +1 objects s)om new 2 KE after = } * (3+2mR2) new ΚΕ, after x (3) + (2) × (3.2) * (0.23) (0.23)2} x (2.112) KE. after 7.446J