A student sits on a rotating stool holding two 3.0 kg objects. When his arms are
ID: 1746513 • Letter: A
Question
A student sits on a rotating stool holding two 3.0 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·m2 and isassumed to be constant. The student then pulls the objectshorizontally to 0.20 m from therotation axis. (a) Findthe new angular speed of the student.rad/s
(b) Find the kinetic energy of the student system before and afterthe objects are pulled in. before J after J (a) Findthe new angular speed of the student.
rad/s
(b) Find the kinetic energy of the student system before and afterthe objects are pulled in. before J after J before J after J
Explanation / Answer
Given that the mass fo the object is m = 3.0 kg The distance between the object and the axis is d = 1.0 m The initial angular speed is 1 = 0.75 rad/s The moment of inertia of the student plus stool is I = 3.0kg·m2 The new distance between the each mass and axis is x = 0.20 m ------------------------------------------------------------------------------------------------- (a) since there isno external force on the system then the angular momentum isconserved . Initial angular momentum = final angular momentum I1*1 = I2*2 ( I + 2md2)1 = ( I +2m*x2)2 2 = ( I +2md2)1 / ( I + 2m*x2) =----------- rad/s This isthe new angular speed of the student (b) The initial kinetic energy is K1= (1/2)I1*12 = (1/2)(I + 2m*d2 )*12 = ------------- J = (1/2)(I + 2m*d2 )*12 = ------------- J Theinitial kinetic energy is K2 = (1/2)I2*22 = (1/2)(I + 2m*x2 )*22 = ------------- J = (1/2)(I + 2m*x2 )*22 = ------------- JRelated Questions
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