Velocity and acceleration in circular motion — A/L Combined Mathematics

How do I practise Velocity and acceleration in circular motion?

1 question with a worked solution

1. A particle moves along a circular path of radius r = 2.0 m with a constant speed v = 6.0 m s⁻¹. What are the magnitudes of its tangential acceleration a_t and centripetal (radial) acceleration a_r?
   1. A) a_t = 18 m s⁻², a_r = 0
   2. B) a_t = 0, a_r = 36 m s⁻²
   3. C) a_t = 0, a_r = 18 m s⁻²
   4. D) a_t = 3 m s⁻², a_r = 18 m s⁻²
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   Correct answer: C) a_t = 0, a_r = 18 m s⁻²

   Since the speed is constant (uniform circular motion), the rate of change of speed is zero: a_t = dv/dt = 0. The centripetal acceleration directed toward the center is a_r = v² / r = (6.0 m s⁻¹)² / (2.0 m) = 36 / 2 = 18 m s⁻².

   Show worked solution

   Step 1: Constant speed => Tangential acceleration a_t = dv/dt = 0. Step 2: Centripetal acceleration a_r = v² / r = 6² / 2 = 18 m s⁻². Answer: a_t = 0, a_r = 18 m s⁻².
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Velocity and acceleration in circular motion fit in the syllabus?

Year 2 · Term 3