A ball is attached to a string that is 1.5m long. It is spun so that it completes two full rotations every second. What is the centripetal acceleration of the ball?

236.63 rad/s²

Explanation:

From simple harmonic motion,

a = ω²r Equation 1

Where a = centripetal acceleration, ω = angular velocity, r = radius of the circle/ length of the string.

Given: r = 1.5 m, ω = 2 rev/s = (2×2π) rad/s = 4π rad/s

Substitute into equation 1

a = (4π)²1.5

a = 16×1.5×π²

a = 24π²

Where the value of π = 3.14,

therefore,

a = 24(3.14)²

a = 236.63 rad/s²

Hence the centripetal acceleration = 236.63 rad/s²

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