Answer, and give a reason. Why does a helicopter with one main rotor need a small tail rotor?
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Answer, and give a reason.
- Why does a helicopter with one main rotor need a small tail rotor?
- A planet moves in an elliptical orbit round the Sun. Where is it fastest?
- A spinning ice skater lifts her arms above her head. What happens to her spin?
Need a reminder? The key ideaShow
Angular momentum: for a body on a fixed axis, and (size ) for a particle. With no external torque, is conserved: . The kinetic energy need not be.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. With no external torque, angular momentum is conserved.
Step 1. (a) The engine turns the rotor one way; by the third law the rotor turns the body the other way. The tail rotor pushes sideways to give an opposite torque and stop the body spinning.
Step 2. (b) The Sun's pull points at the Sun, so it has no torque about it, and is conserved. The planet is fastest where it is closest to the Sun.
Step 3. (c) Raising her arms brings mass closer to the vertical axis, so falls and her spin speeds up.
Answer: (a) To cancel the rotor's reaction torque. (b) At its closest point. (c) She spins faster.
Watch out. In (b) the force is not zero; it is the torque about the Sun that is zero.
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