A toy top with a spool of diameter 5.0 cm has a moment of inertia of 3.0×1025 kg⋅m2 about its rotation axis. To get the top spinning, its string is pulled with a tension of 0.30 N. How long does it take for the top to complete the first five revolutions? The string is long enough that it is wrapped around the top more than five turns

Explanation:

Moment of inertia of toy top = 3 x 10⁻²   kgm²

Torque created = F x r

= .30 x 2.5 x 10⁻² N m

Torque = moment of inertia x angular acceleration

angular acceleration = .3 x 2.5 x 10⁻² / 3 x 10⁻²

α = .25 radian /s²

Angular displacement in 5 revolution θ = 5 x 2π = 10π radian

θ = ω₀t + 1/2 α t²

initial angular velocity ω₀ = 0

10π = 1/2 α t² = .5 x .25 t²

t² = 251.2

t = 15.85 s

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