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Given: Radius of disc, R = 50 cm, Angular acceleration α = 2.0 rad/s², time t = 2 s. Calculate the net acceleration of a particle at the periphery of the disc.

1. a = 8 m/s²
2. a = 10 m/s²
3. a = 6 m/s²
4. a = 12 m/s²

Correct answer: a = 10 m/s²

Solution

The net acceleration of a particle at the periphery of the disc is the vector sum of the tangential acceleration and the centripetal acceleration. Tangential acceleration is given by a_t = αR = (2.0)(0.5) = 1 m/s². Angular velocity after 2 seconds is ω = αt = (2.0)(2) = 4 rad/s. Centripetal acceleration is a_c = ω²R = (4²)(0.5) = 8 m/s². Net acceleration is a = √(a_t² + a_c²) = √(1² + 8²) = √65 ≈ 10 m/s².

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