A car of mass 2000 kg rounds a curve of radius 250 m at 90 km / hr . Compute its, angular speed.

Given: Mass of car, m = 2000 kg Radius of curve, r = 250 m Speed, v = 90 km / hr = 90 × 5 18 = 25 m / s We know angular velocity, ω = v r = 25 250 = 0 . 1 rad / s .

Prove the relation v → = ω → × r → , where symbols have their usual meaning.

We know that angular velocity, ω → = d θ → d t (where θ → is the angular displacement vector) and velocity, v → = d S → d t (where S is the arc length) and length of an arc, S = θ × r . Now, differentiate both the sides with respect to time and we get, d S d t = d ( θ × r ) d t = d θ d t × r ⇒ v → = ω → × r → .

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Is arc length displacement?

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