Goal Apply conservation of angular momentum to a simplesystem.
Problem A student sits on a pivoted stool while holding a pair ofweights. (See Figure) The stool is free to rotate about a verticalaxis with negligible friction. The moment of inertia of student,weights, and stool is 2.25 kg · m2. The student is set in rotationwith arms outstretched, making one complete turn every 1.26 s, armsoutstretched.
Question If the student suddenly releases the weights, how does hisown angular momentum, rotational kinetic energy, and angular speedchange? (Select all that apply.)
His rotational angular speed decreases.
His rotational angular speed remains the same.
His angular momentum remains the same.
His rotational kinetic energy remains the same.
His angular momentum increases.
His angular momentum decreases.
His rotational angular speed increases.
His rotational kinetic energy increases.
His rotational kinetic energy decreases.
A star with an initial radius of 1.00 108 m and period of 30.0 dayscollapses suddenly to a radius of 1.00 104 m.
(a) Find the period of rotation after collapse.
(b) Find the work done by gravity during the collapse if the massof the star is 2.00 1030 kg.
The only force doing work on the system is gravitation, so the workdone by gravitation is the change in kinetic energy of the star.J
(c) What is the speed of an indestructible person standing on theequator of the collapsed star? (Neglect any relativistic or thermaleffects, and assume the star is spherical before and after itcollapses).
HINTS
* Do you expect the initial angular speed to be larger or smallerthan the final angular speed? How is angular speed related toperiod of rotation?
* Is the initial moment of inertia larger or smaller than the finalmoment of inertia?
* Is angular momentum conserved?
* As the star collapses, do you expect the period of rotation tobecome smaller or larger?
Goal Apply conservation of angular momentum to a simplesystem.
Problem A student sits on a pivoted stool while holding a pair ofweights. (See Figure) The stool is free to rotate about a verticalaxis with negligible friction. The moment of inertia of student,weights, and stool is 2.25 kg · m2. The student is set in rotationwith arms outstretched, making one complete turn every 1.26 s, armsoutstretched.
Question If the student suddenly releases the weights, how does hisown angular momentum, rotational kinetic energy, and angular speedchange? (Select all that apply.)
His rotational angular speed decreases.
His rotational angular speed remains the same.
His angular momentum remains the same.
His rotational kinetic energy remains the same.
His angular momentum increases.
His angular momentum decreases.
His rotational angular speed increases.
His rotational kinetic energy increases.
His rotational kinetic energy decreases.
A star with an initial radius of 1.00 108 m and period of 30.0 dayscollapses suddenly to a radius of 1.00 104 m.
(a) Find the period of rotation after collapse.
(b) Find the work done by gravity during the collapse if the massof the star is 2.00 1030 kg.
The only force doing work on the system is gravitation, so the workdone by gravitation is the change in kinetic energy of the star.J
(c) What is the speed of an indestructible person standing on theequator of the collapsed star? (Neglect any relativistic or thermaleffects, and assume the star is spherical before and after itcollapses).
HINTS
* Do you expect the initial angular speed to be larger or smallerthan the final angular speed? How is angular speed related toperiod of rotation?
* Is the initial moment of inertia larger or smaller than the finalmoment of inertia?
* Is angular momentum conserved?
* As the star collapses, do you expect the period of rotation tobecome smaller or larger?
