Question

A torsional oscillator of rotational inertia 1.6 kg⋅m2 and torsional constant 3.4 N⋅m/rad has total energy 4.3 J.

a) What is its maximum angular displacement? Express your answer in radians.

b) What is its maximum angular speed? Express your answer in radians per second.

Answer 1

PART (a):

Maximum displacement is given by:

E_max = 1/2 K θ_max²

(4.3 J) = 1/2 x (3.4 N⋅m/rad) x (θ_max²)

∴ θ_max²) = 4.3 / 1.7

∴ θ_max = 1.304 rad

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Also, Maximum energy = 1/2 Iω²

E_max = 1/2 Iω²

(4.3 J) = 1/2 x ( 1.6 kg⋅m²) x (ω²)

(4.3 J) = (0.8 kg⋅m²) x (ω²)

∴ ω² = 4.3/0.8

∴ ω​​​​​​​ = 2.32 rad/s

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