The torque in this case depends on three variables: the magnitude of the force (F), the distance between the force and the point at which you want to calculate the torque (often called the torsion arm, r), and the angle between the force and the torsion arm (θ). In the above case, the angle between the force and the torsion arm is 90 degrees. Since the sine of 90 equals 1, that gives you the maximum torque for this force and this torsion arm. If you need more torque you can pull harder or you can get a longer wrench with a bigger torsion arm.
But what if you pull with such force that the angle is off the vertical axis? Like that.
If you want to tighten the bolt, it’s a bad idea. You get less torque at this angle (and you would pull the wrench off the nut). In fact, if you let the angle go to zero degrees, you get zero torque. So if you imagine drawing a line through the force at the point of application and that line goes through your torque point (in this case it is the nut), then the torque is zero. Remember that with zero torque you won’t get any change in the rotational motion.
So, by mounting the rocket motor to the top of the rocket, you get zero torque because a line through the force goes through the center of mass and the rocket does not return to a vertical position. But what is different with a real pendulum? The key is the point of rotation. For the free-flight rocket, it can revolve around its center of mass. Neither the gravitational force nor the pushing force of the rocket exert a torque. However, when the top of the rocket is fixed in place (in this first pendulum example), the rocket should rotate around the top point. In this case, the gravitational force is effectively exerting torque and this is what causes it to rock back and forth.
Rocket with thruster at the bottom
OK, you should be able to predict what will happen if I put the rocket thruster on the bottom of the vehicle. In this case, I’m just going to spin the rocket upside down so that the single mass is now at the bottom. Here is what it looks like (and here is the code).
See. It still works. This shows the pendulum rocket error. Putting the rocket motor on top of the vehicle does not bring it back to the upright position, so there is no need to put the motor up there. It makes a lot more sense to have the rocket at the bottom – you know, because all of that hot stuff that’s being shot from the thruster. If you have that at the top, you’re just going to damage your vehicle.
The Iron Man Rocket Fallacy
It’s not about rockets, it’s about Iron Man. In fact, this is a response to some YouTube comments about my appearance on Technical review of WIRED in which I watch the physics of superhero movies. For one of the scenes, I watched the way Iron Man flies (in the movies) using thrusters on his feet and hands. Yes, in the video I did say that “the thrusters on the bottom of a rocket are a bit of a problem” – this is exactly the same pendulum rocket mistake Goddard made with his early designs. Oops. It just feels like the rocket mounted at the bottom would be like holding a vertical pencil from the bottom – but as you can see, that isn’t the case if the rocket is accelerating.