A CD has a mass of 17 g and a radius of 6.0 cm?

Question

When inserted into a player, the CD starts from rest and accelerates to an angular velocity of 20 rad/s in 0.65 s. Assuming the CD is a uniform solid disk, determine the net torque acting on it.

Answer 1

Since we assume that the CD is a uniform disk, the moment of inertia of the CD is

I = 1/2 m r^2

The equation of motion we need is

ω = ωo + α t

ω is the final angular velocity ( 20 rad / s )
ωo is the initial angular velocity ( zero )
α is the angular acceleration ( unknown )
t is the elapsed time ( .65 s )

You know everything except the angular acceleration so solve for α. Then use Newton's Second Law

Γ = I α

where I is the moment of inertia calculated earlier, α the angular acceleration we just found, and Γ is the torque you're looking for.

Answer 2

i think of i may well be useful. The torque required may well be computed utilising right here equation. tau = alpha*Iz the place tau is the torque alpha is the acceleration Iz is the 2nd of inertia for a cylinder utilising reference a million, we see that Iz = a million/2*m*r^2 = 3.06*10^-5 *kg*m^2 the place m = 18 grams r = 6 cm Alpha is the term that demands a splash bit thought. i visit artwork by utilising analogy. If we've been working with linear variables, we can say that vf^2 - vi^2 = 2*a*d the place vf is the astounding speed of an merchandise vi is the preliminary speed of an merchandise a is its acceleration d is the area it strikes. a similar dating exists for angular speed. wf^2 - wi^2= 2*alpha*theta the place wf is the astounding angular speed (450*2*pi/sec) wi is the preliminary angular speed (0 rad/sec) theta is the perspective the item strikes (3*2*pi) fixing for alpha, i'm getting alpha = fifty 8.905 rad/sec^2. Substituting into the preliminary equation, i'm getting tau = 0.0018 N*m