Angular Velocity

Let b1, b2, b3 be a right-handed set of mutually perpendicular unit vectors fixed in a rigid body B. The angular velocity R«B in a reference frame R is defined as

RWB = [(Rdb1/di) • b2]b3 + [(Rdb2/di) • b3]b1 + [(Rdb3/di) • b1]b2

where (Rdbi/di) denotes the ordinary derivative of bi with respect to time in reference frame R. This definition of angular velocity leads to the following results:

Rdb1/di = R«B x b1 Rdb2/di = R«B x b2 Rdb3/di = R«B x b3

Thus, for any vector P defined in the reference frames R and B:

If a series of succesive reference frames is used in the study of motion, the following equation holds:

Velocity and acceleration of two points in a rigid body are related by the following set of equations:

where EaB is the angular acceleration of the rigid body B. The angular acceleration is defined by the relation

Getting Started With Dumbbells

Getting Started With Dumbbells

The use of dumbbells gives you a much more comprehensive strengthening effect because the workout engages your stabilizer muscles, in addition to the muscle you may be pin-pointing. Without all of the belts and artificial stabilizers of a machine, you also engage your core muscles, which are your body's natural stabilizers.

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