Rotation, torques, precession
Angular velocity and acceleration - power and torque. Sponsored Links An electric motor runs with rpm with an measured power consumption of . Here, you'll learn about rotational motion, moments, torque, and angular momentum. Relationship between angular velocity and speed. (Opens a modal). 1. learn to appreciate the similarities, di erences and relationship between Now , for a particle rotating with an angular velocity! about z axis, we also have. 2.
See the section on contact forces. Now let's get quantitative. Mentally, let's divide it up into a collection of small masses.
So let's imagine the dividing the object up into many masses mi at distances ri from the axis. This is the result for a collection of discrete masses, mi. For a continuous body, we should normally divide it up into small elements of volume, dV. You may wish to revise calculus. Students often ask at this stage: Then we just integrate over the limits of x, y and z that define the object being studied. For a sphere or a solid cylinder about their axeshowever, the volume elements would be hollow cylinders about the axis, and the integration would go from zero radius to that of the sphere.
In the examples below, the value for the hoop is obvious: The sphere may be considered as a set of discs with different radii. The rectangle and the disc about its diameter are both analysed as sets of rods. There are examples in most textbooks. I'll put some up here soon, but shall postpone it because it's hard to write maths in html! Moment of inertia Here are some useful common cases that result from the integrals referred to above.
Rolling problems This is one of the puzzles introduced in the multimedia tutorial. Two similar jars, one full of water low viscosity and one full of honey high viscosity. Which one rolls faster?
Torque Formula (Moment of Inertia and Angular Acceleration)
Before your run the film, ask yourself these questions: Assuming their weights are the same, what can you say about their initial potential energies? When they reach the bottom, which will have more rotational kinetic energy?
And therefore, which will have more translational kinetic energy? Essentially, any straight-line motion equation has a rotational equivalent that can be found by making the appropriate substitutions I for m, torque for force, etc.
Example - Falling down You've climbed up to the top of a 7.
Just as you reach the top, the pole breaks at the base. Are you better off letting go of the pole and falling straight down, or sitting on top of the pole and falling down to the ground on a circular path?
- Rotation, torques, precession
- Torque and angular momentum
Or does it make no difference? The answer depends on the speed you have when you hit the ground. The speed in the first case, letting go of the pole and falling straight down, is easy to calculate using conservation of energy: In the second case, also apply conservation of energy.
If you have negligible mass compared to the telephone pole, just work out the angular velocity of the telephone pole when it hits the ground.
In this case we use rotational kinetic energy, and the height involved in the potential energy is half the length of the pole which we can call hbecause that's how much the center of gravity of the pole drops. So, for the second case: Solving for the angular velocity when the pole hits the ground gives: For you, at the end of the pole, the velocity is h times the angular velocity, so: So, if you hang on to the pole you end up falling faster than if you'd fallen under the influence of gravity alone.
This also means that the acceleration of the end of the pole, just before the pole hits the ground, is larger than g 1. Which way do these angular variables point, anyway?
Torque - Wikipedia
Displacement is a vector. Velocity is a vector. Acceleration is a vector. As you might expect, angular displacement, angular velocity, and angular acceleration are all vectors, too.
Torque and Rotational Equilibrium
But which way do they point? Every point on a rolling tire has the same angular velocity, and the only way to ensure that the direction of the angular velocity is the same for every point is to make the direction of the angular velocity perpendicular to the plane of the tire.
To figure out which way it points, use your right hand.