Acd has a mass of 17 g and a radius of 6.0 cm. when inserted into a player, the cd starts from rest and accelerates to an angular velocity of 21 rad / s in 0.8s, assuming the cd is a uniform solid disk. a) determine the sum of the net torque action on it.

the net toque is τ=8.03* 10⁻⁴ N*m

Explanation:

Assuming the disk has constant density ρ, the moment of inertia I of is

I = ∫r² dm

since m = ρ*V = ρπR² h , then dm= 2ρπh r dr

thus

I = ∫r²dm = ∫r²2ρπh r dr =2ρπh ∫r³ dr = 2ρπh (R⁴/4- 0⁴/4)= ρπhR⁴ /2= mR²/2

replacing values

I = mR²/2= 0.017 kg * (0.06 m)²/2 = 3.06 *10⁻⁵ kg*m²

from Newton's second law applied to rotational motion

τ= Iα , where τ=net torque and α= angular acceleration

since the angular velocity ω is related with the angular acceleration through

ω= ωo + α*t → α =(ω-ωo)/t =  (21 rad/s-0)/0.8 s = 26.25 rad/s²

therefore

τ= Iα= 3.06 *10⁻⁵ kg*m²*26.25 rad/s² = 8.03* 10⁻⁴ N*m

the correct choice is a .

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answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.