Problems and solutions I

Rotations are not vectors though vector addition is

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Unformatted text preview: ection of the axis. Rotations are not vectors, though. Vector addition is commutative but rotations are not. It turns out that infinitesimal rotations do commute and are vectors. We can write an infinitesimal ” rotation as „ q. Since angular velocity about an axis requires only an infinitesimal rotation, w = „ q ê „ t, we can define the angular velocity vector w= ” „q „t . There are two possible directions along an axis. We decide which direction by using the right hand rule. Wrap the fingers of your right hand in the direction of rotation. The thumb points in the direction of the vector. If angular velocity is a vector then we can also make angular acceleration a vector. a= „ „t w Wit these considerations we can now make a vector out of the torque. We can assign its direction to the sense of rotation due to that torque. ” ” r and F are vectors; we will define the cross product so that the cross product of r and F is the torque t. 2 | Chapter I - Rotational Dynamics and Equilibrium ” t = räF Interactive Figure The Cross or Vector Product The dot product, or scalar product, is a way of multiplying of two vectors that gives a scalar. The cross product, also known as the vector product, is a multiplication that gives a vector. A ä B is a vect...
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