For 1), what does that value represent? The distance from the center of earth? Or the distance from the surface.

For 2), [itex] F_{G} = \frac{GmM_{e}}{r^{2}} [/itex] is indeed the correct equation to use. The force exerted is the same on both objects but it may seem odd since the apple would be the one moving. The reason it might see non-intuitive is because the earth has such a large mass that the force will have a negligable change on the acceleration of the planet.

While the apple is falling it will still be exerting a force, but that will be changing relative to its distance from the earth.

Hopefully someone else will come along and help with the other problems... my food just arrived.

For 3, I think that energy expression is supposed to have a negative sign in it??? other wise you are just calculating the kinetic energy.

For 5, The blades are spinning at lots of radians per second. To stop in 3 seconds, the angular acceleration would be sufficient to reduce the angular velocity to zero in 3 seconds?

For 4, You need to find how long it takes to travel 1/4 turn while stopping. Note that it will take longer to travel 1/4 turn while stopping than it would to cover a quarter turn while continuing at its original speed.
Once you know that time, you will be able to calculate the accelerations.

thanks for your help guys, i updated my first post with the questions left.
Peter0 i get what your saying, but how would I solve for that, i feel like im forgetting some sort of equation...

edit: nvm angular kinematics equations duh

ALL RIGHT!, all questions done except for this one.

i calculated angular velocity to be 19100.88 and then i divided that by 3, and got 6366.961 however that dosent seem to be the right answer.....

Did you notice the speed of the mower was given in revolutions per minute?

3000+ rpm means 50+ revolutions per second. Each revolution is 2Pi radians - lets say 6 so 300+ radians per second - yep look like you forgot about the minutes.