prove that V is equal to R Omega in uniform circular motion what is its direction of velocity
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First off, if a particle is undergoing circular motion with an angular velocity ω⃗ and the particle has a position vector r⃗ that is measured with respect to an origin that lies on the axis of rotation, then the velocity of the particle is v⃗ =ω⃗ ×r⃗ .
The reason for this (and not doing it the other way around) is purely convention. The way to remember is the right-hand rule. If you point your right thumb in the direction of ω⃗ and then curl your fingers into a fist, your fingers will point in the direction of motion of the object.
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