Which direction is angular momentum

There are three distinct cases for a 3x3 diagonal matrix:. Suppose that the inertia tensor when orthogonalized has three distinct elements and that angular velocity has at least two non-zero elements when expressed in terms of the coordinate system that makes the inertia tensor orthogonal.

Thus there is at least one element of this vector that is non-zero. From matrix algebra, multiplying a n x 1 vector x by an n x n matrix A will scale the vector components in eigenvector direction by respective eigenvalues. Eigenvectors will be aligned to coordinates only when non-diagonal components of A are zero.

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Create a free Team What is Teams? Learn more. Can the direction of angular momentum and angular velocity differ? Ask Question. Asked 4 years, 10 months ago. Active 2 years, 10 months ago. Viewed 3k times. Improve this question.

Emilio Pisanty k 28 28 gold badges silver badges bronze badges. Physicsapproval Physicsapproval 5 5 silver badges 22 22 bronze badges. And the opposite question: physics. The torque produced is perpendicular to the angular momentum, thus the direction of the torque is changed, but not its magnitude. Earth itself acts like a gigantic gyroscope. Its angular momentum is along its axis and points at Polaris, the North Star.

But Earth is slowly precessing once in about 26, years due to the torque of the Sun and the Moon on its nonspherical shape. Rotational kinetic energy is associated with angular momentum? Does that mean that rotational kinetic energy is a vector? No, energy is always a scalar whether motion is involved or not. No form of energy has a direction in space and you can see that rotational kinetic energy does not depend on the direction of motion just as linear kinetic energy is independent of the direction of motion.

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Skip to Content Go to accessibility page. College Physics Using the right hand rule, your right hand would be grasping the pole so that your four fingers index, middle, ring, and pinky are following the direction of rotation. That is, an imaginary arrow from your wrist to your fingertips points in the same direction as the disc is rotating. A gyroscope is a device for measuring or maintaining orientation based on the principles of angular momentum.

Mechanically, a gyroscope is a spinning wheel or disk in which the axle is free to assume any orientation. This direction can be determined using the right hand rule, which says that the fingers on your hand curl towards the direction of rotation or force exerted, and your thumb points towards the direction of angular momentum, torque, and angular velocity.

Direction of Torque and Angular Momentum : In figure a , the torque is perpendicular to the plane formed by r and F and is the direction your right thumb would point to if you curled your fingers in the direction of F. Figure b shows that the direction of the torque is the same as that of the angular momentum it produces.

Rotating wheel: Consider a bicycle wheel with handles attached to it, as in. Suppose the person holding the wheel tries to rotate it as in the figure. Her natural expectation is that the wheel will rotate in the direction she pushes it, however, what happens is quite different. The forces exerted create a torque that is horizontal toward the person, and this torque creates a change in angular momentum L in the same direction, perpendicular to the original angular momentum L, thus changing the direction of L but not the magnitude of L.

The axis of the wheel has thus moved perpendicular to the forces exerted on it, instead of in the expected direction. Gyroscopic Effect : In figure a , a person holding the spinning bike wheel lifts it with her right hand and pushes down with her left hand in an attempt to rotate the wheel. This action creates a torque directly toward her.

The wheel moves toward the person, perpendicular to the forces she exerts on it. Gyroscope: This same logic explains the behavior of gyroscopes see. There are two forces acting on a spinning gyroscope.