Briefly answer the following questions. a) a clock is mounted on the wall. as you look at it, what is the direction of the angular velocity vector of the second hand? what is the value of the angular acceleration of the second hand? b) if the angular acceleration of a rigid body is zero, what is the functional form of the angular velocity? c) what if another planet the same size as earth were put into orbit around the sun along with earth. would the moment of inertia of the system increase, decrease, or stay the same? d) does increasing the number of blades on a propeller increase or decrease its moment of inertia, and why? e) can you think of a body that has the same moment of inertia for all possible axes? if so, give an example, and if not, explain why this is not possible. can you think of a body that has the same moment of inertia for all axes passing through a certain point? if so, give an example and indicate where the point is located. f) to maximize the moment of inertia of a flywheel while minimizing its weight, what shape and distribution of mass should it have? explain. g) is it possible to change the translational) kinetic energy of an object without changing its rotational kinetic energy? what about the reverse of it?

Explanation:

a ) The direction of angular velocity vector of second hand will be along the line going into the plane of dial perpendicular to it.

b )  If the angular acceleration of a rigid body is zero, the angular velocity will remain constant.

c )  If another planet the same size as Earth were put into orbit around the Sun along with Earth  the moment of inertia of the system will increase because the mass of the system increases. Moment of inertia depends upon mass and its distribution around the axis.

d ) Increasing the number of blades on a propeller increases the moment of inertia , because both mass and mass distribution around axis of rotation increases.

e ) It is not possible  that  a body has the same moment of inertia for all possible axes because a body can not remain symmetrical about all axes possible. Sphere has same moment of inertia about all axes passing through its centre.

f ) To maximize the moment of inertia of a flywheel while minimizing its weight, the  shape and distribution of mass should be such that maximum mass of the body may be situated at far end of the body from axis of rotation . So flywheel must have thick outer boundaries and this should be

attached with axis with the help of thin rods .

g ) When the body is rotating at the same place , its translational kinetic   energy is zero but its rotational energy can be increased

at the same place.