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Circular Motion

AP Physics 1· difficulty 3/5

A car rounds a frictionless banked curve at the design speed. The banking angle θ\theta satisfies

  • A

    tan⁡θ=v2/(gr)\tan\theta = v^2/(g r)

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  • B

    cos⁡θ=v/(gr)\cos\theta = v/(g r)

  • C

    tan⁡θ=g/v2\tan\theta = g/v^2

  • D

    sin⁡θ=v2/(gr)\sin\theta = v^2/(g r)

Explanation

Decompose normal force: Nsin⁡θ=mv2/rN\sin\theta = m v^2/r and Ncos⁡θ=mgN\cos\theta = m g. Dividing gives tan⁡θ=v2/(gr)\tan\theta = v^2/(g r).

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