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Re: new problem




An ice-skater is travelling at 11 m/s when she grabs a 32 meter rope attached
to a fixed vertical pole with a radius of 0.20 m. At the instant she
grabs the
rope it is stretched out from the pole, perpendicular to her path.
After she grabs the rope, her path is constrained by the length of the
rope, and she spirals inward toward the pole as the rope winds around it.

At the moment that the free end of the rope is 16 meters long, what is
the speed of the skater?


Is the skater's kinetic energy conserved? Why or why not?

Is the skater's angular momentum conserved? Why or why not?

Howdy,

Neither the Kinetic Energy alone or even the Mechanical Energy (Kinetic +
Potential) are conserved since the force applied through the rope does
(positive) work as the rope spirals inward.

The Angular Momentum also isn't conserved since the Torque due to the
Gravitational Force acting on the person cannot be zero throughout the
motion about any chosen origin.

Here's one of my favorites:

You are given that a Bowling Ball can be considered a uniform solid sphere,
the initial speed of the ball (v) just after release along the alley and
that there is no initial spin of the ball (i.e., it is slipping without
rolling initially). What is the final speed of the ball when it is rolling
without slipping? (Note: there IS kinetic friction between the alley and
the ball.)

The nice thing about this problem is that there is a straight forward way
to attack it (that gives the correct result!) but there is a very
sophisticated was to look at it also.

In general, problems that involve rotational motion are really very nice
because they involve things that students very quickly learn are NOT
intuitive; i.e., their preconceived notions fall apart quickly.

Here's another one:

A uniform solid cubical box of mass M and side length A is sliding without
friction across the surface of the frozen lake. It strikes a stone and
pivots until it is balanced on its edge. What is the initial speed of the
box?

This one is the rotational analog of the ballistic pendulum problem!

Good Luck,


Good

Herb Schulz
(herbs@interaccess.com)