Motion in a horizontal circle — A/L Combined Mathematics

How do I practise Motion in a horizontal circle?

1 question with a worked solution

1. A conical pendulum consists of a small bob of mass m attached to a light inextensible string of length L rotating in a horizontal circle such that the string makes a constant angle θ with the downward vertical. What is the tension T in the string?
   1. A) T = mg / cos θ
   2. B) T = mg sin θ
   3. C) T = mg / sin θ
   4. D) T = mg cos θ
   Check my answer

   Correct answer: A) T = mg / cos θ

   Resolving forces on the bob vertically: since there is no vertical acceleration, the vertical component of string tension balances gravity: T cos θ = mg => T = mg / cos θ. (The horizontal component T sin θ provides the centripetal force m v² / r).

   Show worked solution

   Step 1: Vertical force balance: T cos θ = mg. Step 2: Solve for T: T = mg / cos θ. Answer: T = mg / cos θ.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Motion in a horizontal circle fit in the syllabus?

Year 2 · Term 3