The disc of a pneumatic sander (at

The disc of a pneumatic sander (at left in the photograph above) is used to get the large wheel inside the suitcase spinning. This rather noisy process takes a few minutes. To avoid revealing what is inside the suitcase until the class has had a chance to observe the rather strange behavior of the suitcase, it is best to have it prepared behind the scenes and then slipped into the lecture hall via (one of) the access door(s). Once you have shown the class what happens when you try to turn the suitcase in either direction, you can then undo the latch and open it to reveal the spinning flywheel to them. The flywheel bearing is fairly good, and the wheel can spin for perhaps about 20 minutes, but the rotation does decay, so it is best to have some idea of when you will need this demonstration during your class, and to have it prepared five or ten minutes before then. Oriented as in the photograph above, the flywheel spins in a clockwise direction. So its angular momentum vector, L, points away from the cover, that is, along the axle of the flywheel, from the cover towards the solid back of the suitcase.

Assume that you give the suitcase to a student, who grasps it with the right hand, hinged cover facing outwards. If the student walks in a straight line, the suitcase follows without any odd effects. If the student attempts to make a left turn, the bottom of the suitcase swings inwards, towards the student. If the student makes right turn, the bottom of the suitcase swings outwards, away from the student.

This is similar to what happens with a spinning top, or a gyroscope mounted on a pivot and allowed to precess, which is what happens in the rotating bicycle wheel demonstrations (28.54 -- Bicycle wheel as a top, and 28.57 -- Bicycle wheel precession). As noted above, the flywheel in the suitcase has an angular momentum vector that points perpendicular to the broad faces of the suitcases, from the cover towards the back of the case. In taking the suitcase around a left turn, the student is trying to change the angular momentum vector by rotating it to the left (counterclockwise). It is possible to do this, but it requires the application of a torque, τ = dL/dt. If we imagine how L points at the beginning of the turn and a short time after (dt), we can see that the change in angular momentum, dL, points horizontally, facing backwards (from the student’s perspective). The right hand rule tells us that this torque is counterclockwise, that is, the student must push outwards on the bottom of the suitcase to keep it vertical. Without the application of this torque, the bottom of the suitcase twists inwards, towards the student.

Now, we have the student try to take the suitcase around a right turn. This time, dL points forwards, which means that the torque to keep the suitcase vertical must be clockwise. In the absence of this torque, the bottom of the suitcase moves outwards.

Perhaps if the handle of the suitcase were a vertical rod, or the student could grasp the suitcase at both top and bottom, it would be possible for the student to provide the appropriate torque to keep the suitcase vertical. With the single loop handle at the top, however, this is nearly impossible to do, and it makes for an entertaining demonstration.

The angular momentum of the flywheel, L, is, of course, Iω, where I is the moment of inertia of the flywheel and ω its angular velocity , dθ/dt. (See 28.03 -- Mounted bicycle wheel.) If we call the angle through which L turns as the student attempts to turn the suitcase φ, then in a short time dt, L turns through an angle dφ. Since dφ is small, we can also calculate the magnitude of the torque (if we know L and how fast it is changing direction) by: τ = dL/dt = (L sin dφ)/dt. For small φ, dL is perpendicular to L, so dL = L sin dφ. Also, for a small angle, sin dφ = dφ, so τ = L dφ/dt, or Lω.

An analogy that may aid understanding of the physics of this demonstration is one that you can draw between the torque necessary to change the angular momentum of the suitcase flywheel, and the inward radial force necessary to make an object move in a circle instead of a straight line. In the latter case, one must change the linear momentum, p, of the object, but leave its magnitude unchanged. If we take the tangential velocities of the object before and after a small time interval dt, and call them v1 and v2, we see that dv, (= v2 - v1), and thus dp, points radially inward, perpendicular to the instantaneous linear motion of the object. For the suitcase flywheel, as we saw above, we are trying to change the direction of the angular momentum, L, but leave its magnitude unchanged. If we take this change in direction of angular momentum, dL, over a small time interval dt, we find that it points at right angles to L, so the torque we must apply to accomplish this is perpendicular to L. You can read (from a UCSB-linked computer) a short paper about this analogy here.

Some humor:

Given the odd behavior of

ผลลัพธ์ (อังกฤษ) 2:

The disc of a pneumatic sander (at left in the photograph above) is used to get the large wheel inside the suitcase spinning. This rather noisy process takes a few minutes. To avoid revealing what is inside the suitcase until the class has had a chance to observe the rather strange behavior of the suitcase, it is best to have it prepared behind the scenes and then slipped into the lecture hall via (one of) the access door. (s). Once you have shown the class what happens when you try to turn the suitcase in either direction, you can then undo the latch and open it to reveal the spinning flywheel to them. The flywheel bearing is fairly good, and the wheel can spin for perhaps about 20 minutes, but the rotation does decay, so it is best to have some idea of when you will need this demonstration during your class, and to have it prepared five or. ten minutes before then. Oriented as in the photograph above, the flywheel spins in a clockwise direction. So ITS angular momentum vector, L, points Away from the Cover, that is, along the axle of the Flywheel, from the Cover towards the Solid back of the suitcase. Assume that You give the suitcase to a student, Who grasps it with the. right hand, hinged cover facing outwards. If the student walks in a straight line, the suitcase follows without any odd effects. If the student attempts to make a left turn, the bottom of the suitcase swings inwards, towards the student. If the student Makes Right turn, the bottom of the suitcase swings outwards, Away from the student. This is similar to what happens with a Spinning top, or a Gyroscope mounted on a pivot and allowed to precess, which is what happens in the Rotating. bicycle wheel demonstrations (28.54 - Bicycle wheel as a top, and 28.57 - Bicycle wheel precession). As noted above, the flywheel in the suitcase has an angular momentum vector that points perpendicular to the broad faces of the suitcases, from the cover towards the back of the case. In taking the suitcase around a left turn, the student is trying to change the angular momentum vector by rotating it to the left (counterclockwise). It is possible to do this, but it requires the Application of a torque, t = dL / DT. Imagine if we How at the Beginning of the turn points L and after a short time (DT), that we Can See the Change in angular momentum, dL, points horizontally, Facing backwards (from the student ' s Perspective). The right hand rule tells us that this torque is counterclockwise, that is, the student must push outwards on the bottom of the suitcase to keep it vertical. Without the Application of this torque, the bottom of the suitcase twists Inwards, towards the student. Now, we have the student to take the suitcase TRY Around a Right turn. This time, dL points forwards, which means that the torque to keep the suitcase vertical must be clockwise. In the absence of this torque, the bottom of the suitcase Moves outwards. Perhaps if the Handle of the suitcase were a Vertical Rod, or the student could grasp the suitcase at both top and bottom, it would be possible for the student to provide the. appropriate torque to keep the suitcase vertical. With the single loop Handle at the top, however, this is nearly Impossible to do, and it Makes for an entertaining demonstration. The angular momentum of the Flywheel, L, is, of course, I omega , where I is the Moment of inertia. of the Flywheel and omega ITS angular Velocity, D theta / DT. (See 28.03 - Mounted Bicycle wheel.) If we Angle Through the Call which L Turns as the student Attempts to turn the suitcase phi , then in a short time DT, L Turns Through an Angle D phi . Since D phi is Small,. Can we also Calculate the magnitude of the torque (if we know it is changing direction L and How fast) by: t = dL / DT = (L Sin D phi ) / DT. For Small phi , dL is Perpendicular to L, so dL = L Sin D phi . Also, for a Small Angle, Sin D phi = D phi , so t = L D phi / DT, or L omega . An analogy that May Aid. understanding of the physics of this demonstration is one that you can draw between the torque necessary to change the angular momentum of the suitcase flywheel, and the inward radial force necessary to make an object move in a circle instead of a straight line. In the latter case, one must change the linear momentum, p, of the object, but leave its magnitude unchanged. If we take the tangential velocities of the object before and after a small time interval dt, and call them v1 and v2, we see that dv, (= v2 - v1), and thus dp, points radially inward, perpendicular to the instantaneous linear. motion of the object. For the suitcase flywheel, as we saw above, we are trying to change the direction of the angular momentum, L, but leave its magnitude unchanged. If we take this change in direction of angular momentum, dL, over a small time interval dt, we find that it points at right angles to L, so the torque we must apply to accomplish this is perpendicular to L. You can read (from. a UCSB Computer-linked) a short Paper About this analogy here. Some humor: Given the behavior of Odd.

ผลลัพธ์ (อังกฤษ) 3:

The disc of a pneumatic sander (at left in the photograph above) is used to get the large wheel inside the suitcase, spinning. This rather noisy process takes a few minutes. To avoid revealing what is inside the suitcase until the class has had a. Chance to observe the rather strange behavior of the suitcase it is, best to have it prepared behind the scenes and then. Slipped into the lecture hall via (one of) the access door (s). Once you have shown the class what happens when you try to. Turn the suitcase in, either direction you can then undo the latch and open it to reveal the spinning flywheel to, them. The flywheel bearing is, fairly good and the wheel can spin for perhaps about 20 minutes but the, rotation, does decay so. It is best to have some idea of when you will need this demonstration during your class and to, have it prepared five or. Ten minutes before then. Oriented as in the, photograph above the flywheel spins in a clockwise direction. So its angular. Momentum vector L points away from the,,,, cover that is along the axle of the flywheel from the, cover towards the solid. Back of the suitcase.Assume that you give the suitcase to a student who grasps, it with the right hand hinged cover, facing outwards. If the. Student walks in a straight line the suitcase, follows without any odd effects. If the student attempts to make a, left turn. The bottom of the suitcase swings inwards towards the, student. If the student makes right turn the bottom, of the suitcase. Swings outwards away from, the student.This is similar to what happens with a, spinning top or a gyroscope mounted on a pivot and allowed to precess which is,, What happens in the rotating bicycle wheel demonstrations (28.54 - Bicycle wheel as, a top and 28.57 - Bicycle wheel precession).? As noted above the flywheel, in the suitcase has an angular momentum vector that points perpendicular to the broad faces. Of, the suitcases from the cover towards the back of the case. In taking the suitcase around a left turn the student, is. Trying to change the angular momentum vector by rotating it to the left (counterclockwise). It is possible to, do this but. It requires the application of, a torque τ = dL / dt. If we imagine how L points at the beginning of the turn and a short. Time after (DT), we can see that the change in angular momentum dL points horizontally facing,,, backwards (from the student s. " Perspective). The right hand rule tells us that this torque, is counterclockwise that is the student, must push outwards. On the bottom of the suitcase to keep it vertical. Without the application of this torque the bottom, of the suitcase twists. Inwards towards the, student.Now we have, the student try to take the suitcase around a right turn. This time dL forwards, points, means which that. The torque to keep the suitcase vertical must be clockwise. In the absence of this torque the bottom, of the suitcase moves. Outwards.Perhaps if the handle of the suitcase were a vertical rod or the, student could grasp the suitcase at both top, and bottom. It would be possible for the student to provide the appropriate torque to keep the suitcase vertical. With the single loop. Handle at, the top however this is, nearly impossible to do and it, makes for an entertaining demonstration.The angular momentum of the flywheel L is,,,,, of course I conductivity where I is the moment of inertia of the flywheel and conductivity its. Angular, velocity D θ / dt. (See 28.03 - Mounted bicycle wheel.) If we call the angle through which L turns as the student. Attempts to turn the suitcase φ then in, a short, time DT L turns through an angle D φ. Since D φ is small we can, also calculate. The magnitude of the torque (if we know L and how fast it is changing direction) by: τ = dL / dt = (L sin D φ) / dt. For small. φ dL is, perpendicular, to L so dL = L sin D φ. Also for a, small angle sin D, φ = D, φ so τ = L D φ / dt or, L conductivity.An analogy that may aid understanding of the physics of this demonstration is one that you can draw between the torque. Necessary to change the angular momentum of the suitcase flywheel and the, inward radial force necessary to make an object. Move in a circle instead of a straight line. In the, latter case one must change the linear momentum P of object the,,,, But leave its magnitude unchanged. If we take the tangential velocities of the object before and after a small time interval. DT and call, them V1 and V2 we see, that DV, (= V2 - V1), and thus DP points radially, inward perpendicular to, the instantaneous. Linear motion of the object. For the, suitcase flywheel as we saw above we are, trying to change the direction of the angular. ,, momentum L but leave its magnitude unchanged. If we take this change in direction of angular momentum dL over a small,,, Time interval DT we find, that it points at right angles, to L so the torque we must apply to accomplish this is perpendicular. To L. You can read (from a UCSB-linked computer) a short paper about this analogy here.Some.