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Angular inert is a vector and, therefore, *has direction and magnitude*. Torque affects both the direction and the magnitude of angular momentum. What is the direction that the angular momentum of a rotating object favor the disc in number 1? The figure shows the * right-hand rule* used to discover the direction the both angular momentum and angular velocity. Both **L** and also **ω** are vectors—each has actually direction and magnitude. Both can be represented by arrows. The right-hand rule defines both to it is in perpendicular come the aircraft of rotation in the direction shown. Due to the fact that angular momentum is related to angular velocity by **L = Iω**, the direction that

**L**is the very same as the direction of

**ω**. Notification in the number that both suggest along the axis the rotation.

Figure 1. Figure (a) shows a decaying is rotating counterclockwise as soon as viewed from above. Figure (b) mirrors the right-hand rule. The direction of angular velocity **ω** size and also angular momentum **L** are defined to it is in the direction in i beg your pardon the thumb of your appropriate hand points once you curl her fingers in the direction the the disk’s rotation together shown.

Now, recall that torque alters angular momentum together expressed by

This equation method that the direction of **ΔL** is the same as the direction of the torque **τ** that creates it. This an outcome is depicted in figure 2, which mirrors the direction of torque and also the angular inert it creates. Let united state now consider a bicycle wheel through a couple of handle attached to it, as shown in figure 3. (This device is renowned in demonstrations among physicists, since it does unforeseen things.) v the wheel rotating together shown, that is angular inert is to the woman’s left. Mean the human being holding the wheel do the efforts to rotate it together in the figure. Her natural expectation is that the wheel will rotate in the direction she pushes it—but what happens is fairly different. The forces exerted produce a torque that is horizontal towards the person, as shown in figure 3(a). This torque create a adjust in angular momentum **L** in the very same direction, perpendicular come the initial angular momentum **L**, thus changing the direction the **L** however not the size of **L**. Number 3 shows how** ΔL** and also **L** add, giving a brand-new angular momentum with direction that is inclined much more toward the person than before. The axis that the wheel has thus moved *perpendicular to the forces exerted on it*, rather of in the intended direction.

Figure 2. In figure (a), the talk is perpendicular to the airplane formed through r and** F** and also is the direction your best thumb would point to if friend curled your fingers in the direction that **F**. Number (b) mirrors that the direction that the torque is the exact same as that of the angular momentum it produces.

Figure 3. In figure (a), a human being holding the spinning cycle wheel lifts it v her best hand and also pushes down through her left hand in an effort to turn the wheel. This activity creates a torque directly toward her. This torque reasons a change in angular momentum **ΔL** in precisely the very same direction. Figure (b) shows a vector diagram depicting how **ΔL** and also **L** add, creating a brand-new angular inert pointing an ext toward the person. The wheel moves towards the person, perpendicular come the pressures she exerts ~ above it.

This exact same logic defines the behavior of gyroscopes. Figure 4 shows the two forces acting top top a rotate gyroscope. The torque developed is perpendicular come the angular momentum, thus the direction of the speak is changed, yet not its magnitude. The gyroscope *precesses* about a vertical axis, since the talk is constantly horizontal and also perpendicular come **L**. If the gyroscope is *not* spinning, it repurchase angular inert in the direction of the speak (**L = ΔL**), and also it rotates about a horizontal axis, fallout’s over just as we would certainly expect. Earth itself acts choose a huge gyroscope. That is angular inert is follow me its axis and also points at Polaris, the north Star. However Earth is slowly precessing (once in about 26,000 years) due to the speak of the Sun and the Moon ~ above its nonspherical shape.

Figure 4. As checked out in number (a), the forces on a turn gyroscope room its weight and the supporting pressure from the stand. This forces create a horizontal torque on the gyroscope, which develop a readjust in angular momentum **ΔL** that is additionally horizontal. In number (b), **ΔL** and** L** include to develop a brand-new angular momentum through the exact same magnitude, yet different direction, so the the gyroscope precesses in the direction shown instead of fallout’s over.

Rotational kinetic power is connected with angular momentum? go that mean that rotational kinetic power is a vector?

**Solution**

No, energy is always a scalar whether motion is involved or not. No kind of power has a direction in an are and you deserve to see that rotational kinetic energy does not depend on the direction the motion simply as straight kinetic energy is live independence of the direction that motion.

## Section Summary

Torque is perpendicular to the aircraft formed by*r*and also

**F**and also is the direction your appropriate thumb would suggest if you curled the finger of your appropriate hand in the direction of

**F**. The direction of the talk is hence the same as that of the angular inert it produces.The gyroscope precesses about a vertical axis, because the speak is always horizontal and also perpendicular come

**L**. If the gyroscope is no spinning, it repurchase angular momentum in the direction of the torque (

1. If driving his motorcycle in ~ highway speed, a physics college student notices the pulling ago lightly ~ above the ideal handlebar tips the cycle to the left and also produces a left turn. Describe why this happens.

2. Gyroscopes supplied in guidance solution to indicate directions in an are must have actually an angular momentum the does not change in direction. Yet they are often subjected to huge forces and accelerations. How can the direction of your angular momentum be continuous when they room accelerated?

1.** incorporated Concepts**

The axis of earth makes a 23.5° angle through a direction perpendicular to the plane of earth orbit. As shown in number 6, this axis precesses, make one complete rotation in 25,780 y.

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(a) calculation the readjust in angular inert in half this time.(b) What is the mean torque developing this change in angular momentum?(c) If this talk were created by a solitary force (it is not) acting at the most effective allude on the equator, what would certainly its magnitude be?

Figure 6. The earth axis slowly precesses, constantly making an edge of 23.5° v the direction perpendicular come the plane of earth’s orbit. The readjust in angular momentum because that the two presented positions is fairly large, return the size **L** is unchanged.

## Glossary

right-hand rule:direction the angular velocity ω and also angular momentum L in i m sorry the ignorance of your appropriate hand points as soon as you curl her fingers in the direction of the disk’s rotation### Selected options to difficulties & Answers

1. (a) 5.64 × 1033 kg ⋅ m2/2 (b) 1.39 × 1022 N ⋅ m (c) 2.17 × 1015 N