A computer hard disk manufactured by the Acme Computer Peripherals (W.E. Coyote,

Question

A computer hard disk manufactured by the Acme Computer Peripherals (W.E. Coyote, President) is 3 cm in diameter, has a mass of 18 g and spins up to 1000 rpm in 2.3 s a.) (2 pts.) What is the angular acceleration of the disk? b.) (2 pts.) What is the angular velocity of the disk at 2.3 s (expressed in radians/sec)? c.) (2 pts.) What is the linear velocity of a point on the rim of the disk? d.) (2 pts.) Assuming the angular acceleration is constant, what is the torque applied to the disk to spin it up?

Explanation / Answer

r = 3/2 = 1.5 cm = 0.015 m.

(a) w = 1000 rpm = (1000*2*3.141) / 60 = 104.7 rad/s.

t = 2.3 s

apply the expression -

w = w0 + alfa*t

=> 104.7 = 0 + alfa*2.3

=> alfa = 104.7/2.3 = 45.5 rad/s^2

(b) As calculated above, w = 104.7 rad/s

(c) Linear velocity, v = w*r = 104.7*0.015 = 1.57 m/s

(d) Moment of inertia of the disc, I = (1/2)*m*r^2 = 0.5*0.018*0.015^2 = 2.03 x 10^-6 kg.m^2

So, torque T = I*alfa = 2.03 x 10^-6 x 45.5 = 9.21 x 10^-5 N.m

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