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Newton's Laws for Rotation

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Contents:   ● Linear & Rotational Equiv.   ● Rotational Form of Newton's Laws   ● Torque & Precession

Using our equivalence table, we can state the rotational motion equivalents of Newton's laws of motion:

Newton Rotational I The rotational principle of inertia: In the absence of a net applied torque, the angular velocity remains unchanged.
Newton Rotational II

τ = I α

This is not as general a relationship as the linear one because the moment of inertia, I, is not strictly a scalar quantity. The rotational equation is limited to rotation about a single principal axis, which in simple cases is an axis of symmetry.

Newton Rotational III  For every applied torque, there is an equal and opposite reaction torque. (A result of Newton's 3rd law of linear motion.)

While torque can be defined through this relationship since we know about moment of inertia, it can also be useful to understand the concept of torque as it derives from force. The size and direction of the torque τ produced by a force F depends on where the force is applied relative to the rotation axis.

Diagram of the right hand rule.

It follows something known as the right hand rule for the vector cross-product. The torque is largest when the force F works at right angles to the object being spun.

Unlike (linear) force, the direction of the torque does not directly tell us which way the object is going to move. Instead, it tells the rotation axis direction for the angular acceleration. If the torque rotation axis lines up with the rotation axis the object is already spinning around, its angular velocity axis, the object's rotation speed will change (it's spin will speed up or slow down). But if the torque rotation axis points along a different direction from the object's spin axis, then the torque will change the direction of the spin axis - the object precesses.

Return to linear & rotational equivalents. Go to torque & precession.

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