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  • Describe the right-hand rule to find the direction of angular velocity, momentum, and torque.
  • Explain the gyroscopic effect.
  • Study how Earth acts like a gigantic gyroscope.

Angular momentum is a vector and, therefore, has direction as well as magnitude . Torque affects both the direction and the magnitude of angular momentum. What is the direction of the angular momentum of a rotating object like the disk in [link] ? The figure shows the right-hand rule    used to find the direction of both angular momentum and angular velocity. Both L size 12{L} {} and ω size 12{ω} {} are vectors—each has direction and magnitude. Both can be represented by arrows. The right-hand rule defines both to be perpendicular to the plane of rotation in the direction shown. Because angular momentum is related to angular velocity by L = I ω size 12{L=Iω} {} , the direction of L size 12{L} {} is the same as the direction of ω size 12{ω} {} . Notice in the figure that both point along the axis of rotation.

In figure a, a disk is rotating in counter clockwise direction. The direction of the angular momentum is shown as an upward vector at the centre of the disk. The vector is labeled as L is equal to I-omega. In figure b, a right hand is shown. The fingers are curled in the direction of rotation and the thumb is pointed vertically upward in the direction of angular velocity and angular momentum.
Figure (a) shows a disk is rotating counterclockwise when viewed from above. Figure (b) shows the right-hand rule. The direction of angular velocity ω size and angular momentum L are defined to be the direction in which the thumb of your right hand points when you curl your fingers in the direction of the disk’s rotation as shown.

Now, recall that torque changes angular momentum as expressed by

net τ = Δ L Δ t . size 12{"net "τ= { {ΔL} over {Δt} } } {}

This equation means that the direction of Δ L size 12{ΔL} {} is the same as the direction of the torque τ size 12{τ} {} that creates it. This result is illustrated in [link] , which shows the direction of torque and the angular momentum it creates.

Let us now consider a bicycle wheel with a couple of handles attached to it, as shown in [link] . (This device is popular in demonstrations among physicists, because it does unexpected things.) With the wheel rotating as shown, its angular momentum is to the woman's left. 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—but what happens is quite different. The forces exerted create a torque that is horizontal toward the person, as shown in [link] (a). This torque creates a change in angular momentum L size 12{L} {} in the same direction, perpendicular to the original angular momentum L size 12{L} {} , thus changing the direction of L size 12{L} {} but not the magnitude of L size 12{L} {} . [link] shows how Δ L size 12{ΔL} {} and L size 12{L} {} add, giving a new angular momentum with direction that is inclined more toward the person than before. The axis of the wheel has thus moved perpendicular to the forces exerted on it , instead of in the expected direction.

In figure a, a plane is shown. Force F, lying in the same plane, is acting at a point in the plane. At a point, at distant-r from the force, a vertical vector is shown labeled as tau, the torque. In figure b, there is a child on a horse on a merry-go-round. The radius of the merry-go-round is r units. At the foot of the horse, a vector along the plane of merry-go-round is shown. At the centre, the direction of torque tau, angular velocity omega, and angular momentum L are shown as vertical vectors.
In figure (a), the torque is perpendicular to the plane formed by r size 12{r} {} and F size 12{F} {} and is the direction your right thumb would point to if you curled your fingers in the direction of F size 12{F} {} . Figure (b) shows that the direction of the torque is the same as that of the angular momentum it produces.

In figure a, a lady is holding the spinning bike wheel with her hands. The wheel is rotating in counter clockwise direction. The direction of the force applied by her left hand is shown downward and that by her right hand in upward direction. The direction of angular momentum is along the axis of rotation of the wheel. In figure b, addition of two vectors L and delta-L is shown. The resultant of the two vectors is labeled as L plus delta L. The direction of rotation is counterclockwise.
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. This torque causes a change in angular momentum Δ L in exactly the same direction. Figure (b) shows a vector diagram depicting how Δ L and L add, producing a new angular momentum pointing more toward the person. The wheel moves toward the person, perpendicular to the forces she exerts on it.

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Source:  OpenStax, Physics 101. OpenStax CNX. Jan 07, 2013 Download for free at http://legacy.cnx.org/content/col11479/1.1
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