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A particle moves along a circle under the action of a single force that always points toward a fixed point O located on the circumference of the circle. If theta is the angle subtended at O by the arc from O to the particle's current position, find the ratio (d²*theta/dt²) / (d*theta/dt)².
- tan(theta) / 2
- 4*tan(theta)
- tan(theta)
- 2*tan(theta)
Correct answer: 2*tan(theta)
Solution
Setting up tangential and centripetal equations with arc length s = 2R*theta and the angle geometry gives (d²*theta/dt²)/(d*theta/dt)² = 2*tan(theta).
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