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NECO 2005 Physics · Question 18

A body moves along a circular path with uniform angular speed of 0.6 rad s-1 and at a constant speed of 3.0…

Question

A body moves along a circular path with uniform angular speed of 0.6 rad s-1 and at a constant speed of 3.0 ms−1ms^{-1}. Calculate the acceleration of the body towards the centre of the circle.

  1. A.0.2.ms−2ms^{-2}
  2. B.1.8 ms−2ms^{-2}
  3. C.5.0 ms−2ms^{-2}
  4. D.5.4 ms−2ms^{-2}
  5. E.25.0 ms−2ms^{-2}

Answer: B. 1.8 ms−2ms^{-2}

Explanation written with AI and checked against the answer key

Analyze the question: The body moves in a circle with angular speed ω = 0.6 rad/s and linear speed v = 3.0 m/s. We need the centripetal acceleration (the acceleration towards the centre). Concept: Centripetal acceleration can be written in these equivalent forms: a = v²/r = ω²r = ωv The last form, a = ωv, is useful here because both ω and v are given, so we don't need to find r first. Solution: Step 1: Find the radius using v = ωr: r = v/ω = 3.0 / 0.6 = 5.0 m Step 2: Find the centripetal acceleration: a = v²/r = (3.0)² / 5.0 = 9 / 5 = 1.8 m/s² Check with a = ωv = 0.6 × 3.0 = 1.8 m/s² ✓ Answer: The acceleration towards the centre is 1.8 m/s². Tip: When a circular motion question gives both ω and v, use a = ωv directly and skip finding r. Watch out for option C (5.0), which is the radius, not the acceleration. Examiners often include the intermediate value as a distractor.

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