What happens if angular momentum and torque are perpendicularr?
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Torque and angular momentum are perpendicular to the direction of force/momentum by convention. In other words, it is a pragmatic but otherwise arbitrary decision.
Part of what we are trying to indicate with a cross product vector for torque or angular momentum is the direction of rotation — e.g. whether it is clockwise or counter-clockwise — but the direction of rotation is only meaningful relative to the plane the object is rotating in. Think about a bicycle wheel. If the wheel is rotating clockwise from our perspective, and we then spin the handlebars 180°, the wheel is suddenly rotating counter-clockwise from our perspective. The wheel hasn’t changed its direction of rotation in any meaningful sense, obviously, but the plane of its rotation has shifted 180°. In fact, the only consistent perspective on the direction of rotation of a wheel is from the perspective of its axle:
No matter which way we turn the wheel, it will still be spinning in the same direction with respect to its axle. And so we make the right-hand-rule convention: we use one vector if the wheel is spinning one way with respect to the axle (counter-clockwise means thumb pointing up, or at us), and the opposite vector if the wheel is spinning the other way (clockwise means thumb pointing down, or away from us).
torque is represented by the large yellow arrow, and angular momentum by the smaller purple arrow. Note that they are out of phase by one-quarter cycle because torque is maximum as the swinging arm accelerates while angular momentum is maximum when acceleration ceases and the arm begins to slow.
This conventional vector tells us three meaningful and useful things:
It has a magnitude that gives the size of the effect: the magnitude of angular momentum/torqueIt has an orientation vector that is orthogonal (perpendicular) to the plane the object is rotating in, and thus defines the plane absolutelyIt has a positive/negative (up/down) value that indicates the direction of rotation with respect to that plane.
So, by constructing torque/angular momentum as a vector perpendicular to the plane of rotation, we are able to fully describe the rotation of the object: the magnitude of rotation, the plane it is rotating on, and the direction of rotation within that plane
hope you understand
Part of what we are trying to indicate with a cross product vector for torque or angular momentum is the direction of rotation — e.g. whether it is clockwise or counter-clockwise — but the direction of rotation is only meaningful relative to the plane the object is rotating in. Think about a bicycle wheel. If the wheel is rotating clockwise from our perspective, and we then spin the handlebars 180°, the wheel is suddenly rotating counter-clockwise from our perspective. The wheel hasn’t changed its direction of rotation in any meaningful sense, obviously, but the plane of its rotation has shifted 180°. In fact, the only consistent perspective on the direction of rotation of a wheel is from the perspective of its axle:
No matter which way we turn the wheel, it will still be spinning in the same direction with respect to its axle. And so we make the right-hand-rule convention: we use one vector if the wheel is spinning one way with respect to the axle (counter-clockwise means thumb pointing up, or at us), and the opposite vector if the wheel is spinning the other way (clockwise means thumb pointing down, or away from us).
torque is represented by the large yellow arrow, and angular momentum by the smaller purple arrow. Note that they are out of phase by one-quarter cycle because torque is maximum as the swinging arm accelerates while angular momentum is maximum when acceleration ceases and the arm begins to slow.
This conventional vector tells us three meaningful and useful things:
It has a magnitude that gives the size of the effect: the magnitude of angular momentum/torqueIt has an orientation vector that is orthogonal (perpendicular) to the plane the object is rotating in, and thus defines the plane absolutelyIt has a positive/negative (up/down) value that indicates the direction of rotation with respect to that plane.
So, by constructing torque/angular momentum as a vector perpendicular to the plane of rotation, we are able to fully describe the rotation of the object: the magnitude of rotation, the plane it is rotating on, and the direction of rotation within that plane
hope you understand
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