Question

1.explain why changing the axis of rotation of an object chances its monent of inertia ?

2. Why does a long pole help a tightrope walker stay balanced?

3. Stars orginate as large bodies of slowly rotating gas. Because of gravity, these clumps of gas decrease in size . What happens to the angular speed of a star as shrinks?explain.

Answer 1

1) Moment of inertia is the name given to rotational inertia, the rotational analog of mass for linear motion. It appears in the relationships for the dynamics of rotational motion. The moment of inertia must be specified with respect to a chosen axis of rotation. For a point mass the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis, I = mr². That point mass relationship becomes the basis for all other moments of inertia since any object can be built up from a collection of point masses.

2) it is related to the angular momentum of the pole.

It is easy to understand that It would take a lot of energy to start the pole twirling like a baton, and that the longer the pole, the more effort it would take to twirl it - to get it to rotate.

You can look at it slightly differently in seeing that the pole has a high moment of inertia, and therefore angular momentum; that is, it 'resists' being rotated, and once it begins to rotate, resists having the speed of rotation changed. Slightly adapting Newton's law: "an object that is not in rotation will continue to not rotate unless there is a rotational force applied to it"

More technically, since the moment of inertia of the pole is large, it takes a lot of force to accelerate the pole in a rotation movement.

The acrobat can use that to counterbalance his or her own motion, since if they apply force to rotate the pole counterclockwise, they would 'experience' the countering force: a clockwise force. So if they start to fall left (to rotate counterclockwise), if they rotate the pole left, they will be 'rotated' right.

Of course, once they put energy into the pole's rotation, they have to counter the poles momentum to stop it from rotating, so they have to lean the right way to be able to do that, but that is part of the skill one has to develop to be a successful (and surviving) acrobat.

3) The angular speed must increase. Since gravity does not exert a torque on the system, its angular momentum remains constant as the gas contracts.