Through conservation of angular momentum, as moment of inertia decreases, the angular velocity increases. Moment of inertia is dependent on the distribution of the spinning body's mass away from the center of mass—as the skater brings his arms in, he lowers his moment of inertia, thus increasing his angular velocity. If he raises his arms completely vertically from this point, it does not change the radius of mass distributions (from the center of his body), thus maintaining his angular velocity.

By the conservation of angular momentum, the angular momentum , is equal to the product of the mass, angular velocity, and radius (or length of the rope in this case). The equation relating these terms is:

Here,  is the initial mass,  is the initial angular velocity, and  is the length of the rope, which remains constant. Angular momentum must be conserved, thus: 

Substitute.

We are given that  and  is the final velocity. Plug in and solve.

Since the platform is frictionless, as the child walks, angular momentum is conserved. However, since there is an  term in the kinetic energy expression, as  decreased due to the increase of inertia, it affects the energy more, and it decreases. From the reference frame of the disk, the child feels an outward directed force, and thus is doing negative work. This is the same principle that allows ice skaters to increase their spinning speed.

For the first disk, we have the information below.

For the second disk, we have the information below.

(The minus sign indicates counterclockwise while the positive indicates clockwise.)

To do this problem, we use conservation of angular momentum. Before the disks are put in contact, the initial total angular momentum is given by the equation below.

It is just the sum of the angular momentums of each disk. When the disks are combined together, then final angular momentum can be found by the following equation.

Set this equal to the initial angular momentum.

Simplify and solve for .

The equation for conservation of angular momentum is:

This means that the angular momentum of the object at the two points in its orbit must be the same. Since the mass of the debris does not change, this gives us an equality of the product of the velocity and distance of the debris at any two points of its orbit:

Plug in known values.

There is disagreement between units; the velocities are given in both  and . Glance down at the answer choices and note that they are all lengths in kilometers.

Solve for : 

Remember the torque equation:

Exerting force on the wrench at an angle less perpendicular to the wrench will reduce and thus reduce the torque.

The other answer options will all increase the torque being applied, making the twisting motion easier.

"Weightlessness" is analogous to free-fall (neglecting air resistance), during which the only force on an object is the force of gravity. When normal force becomes zero, the object loses physical contact with the surface.

When normal force is equal to the force of gravity, the object is in equilibrium and the net vertical force is zero. This results in zero acceleration, but does not result in "weightlessness." Mass is not a force, and negative force values merely indicate relative direction (assuming correct calculations)

Frictional force is calculated using the normal force and the friction coefficient. Since the book is at rest (not in motion), we use the coefficient of static friction.

The normal force will be equal and opposite the force pushing directly into the surface; in this case, that means the normal force will be 20N.

Solve for the force of friction: