Question

When the play button is pressed, a CD accelerates uniformly from rest to 450 rev/min in 3.0 revolutions. If the CD has a radius of 7.0 cm and a mass of 15 g , what is the torque exerted on it? Express your answer using two significant figures.

Answer 1

Consider CD as a disk,

Moment of inertia is,

I = Mr²/2

= (0.015 kg)(0.07 m)²/2

= 3.675x10^-5 kgm²

now,

ω_f² = ω_i² + 2αθ

[(450x2π)/(60 s)]² = 0² + 2α(3x2π)

or, α = 58.9 rad/s²

torque is,

τ = Iα

= (3.675x10^-5 kgm²)(58.9 rad/s²)

= 2.2x10^-5 N.m

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