A2L Item 069
- Description: Find final angular velocity when rock is thrown tangentially from a rotating platform initially at rest.
- Goal: Problem solving.
- Source: UMPERG-ctqpe146
- Keywords: Angular Momentum, Angular Velocity, Conservation, Mechanics, Problem Solving, Rotational Motion
The question for students:
A
child having mass 32kg is standing at the rim of a rotating disk of
radius 1.5m. The disk is free to rotate without friction. The disk has
moment of inertia I = 125kg-m2 and is initially at rest. The
child throws a rock of mass 4kg in the forward tangential direction as
shown in the figure with a speed of 5m/s. The final angular speed of
the disk is most nearly
- 0.10 rad/s
- -0.25 rad/s
- 0.41 rad/s
- 1.5 rad/s
- -1.0 rad/s
- 0.50 rad/s
- -0.15 rad/s
- None of the above
- Cannot be determined
Commentary for teachers:
Answer
(7) is the most appropriate response. Initially there is no angular momentum in the system. The child and disk must rotate clockwise to balance the angular momentum of the rock. Some students may forget to add the moment of inertia of child to that of the disk.
Background
Throwing the rock tangentially gives the rock angular momentum relative to the fixed center of the disk. The disk-child system must have an angular momentum which is the negative of that of the rock. Thus, it is possible to find the angular velocity. The angular velocity is negative, i,e, into the page.
Questions to Reveal Student Reasoning
Does the total system have angular momentum just before the rock is thrown? just after it is thrown?
Does the rock have angular momentum just before it is thrown? just after it is thrown?
What happens to the child upon throwing the rock? Does the child move? How?
Suggestions
Have students relate their answer to this question to items 67 and 68.