7. What is the kinetic energy of a music CD if it has a mass of 12 g, a radius o

Question

7. What is the kinetic energy of a music CD if it has a mass of 12 g, a radius of 6.0 cm, and it spins in a CD player at 325 rpm. You can treat the CD as a uniform disk.

8. Calculate the rotational kinetic energy of a 7.5-kg bowling ball with a radius of 11 cm if it rolls without slipping at a rate of 3.1 m/s down a bowling lane. What is the total kinetic energy of the ball?

**please guide me through**

7. What is the kinetic energy of a music CD if it has a mass of 12 g, a radius of 6.0 cm, and it spins in a CD player at 325 rpm. You can treat the CD as a uniform disk. 8. Calculate the rotational kinetic energy of a 7.5-kg bowling ball with a radius of 11 cm if it rolls without slipping at a rate of 3.1 m/s down a bowling lane. What is the total kinetic energy of the ball?

Explanation / Answer

(7) Moment of inertia of the disk, I = (1/2)*m*r^2 = 0.5x12x10^-3x0.06^2 = 2.16 x 10^-5 kg.m^2

now, w = 325 rpm = (325x2x3.1411) / 60 = 34.03 rad/s

So, kinetic energy of the music CD = (1/2)*I*w^2 = 0.5*2.16 x 10^-5*34.03^2 = 1.25 x 10^-2 J

(8) Given that -

m = 7.5 kg, r = 0.11 m, v = 3.1 m/s

So, angular velocity w = v/r = 3.1/0.11 = 28.2 rad/s

Now, moment of inertia of the ball, I = (2/5)*m*r^2

So, rotational kinetic energy, Ir = (1/2)*I*w^2 = (1/2)*(2/5)*m*r^2*w^2

put the values -

Ir = 0.5*0.4*7.5*0.11^2*28.2^2 = 14.41 J

Total kinetic energy, It = Ir + Ik = 14.41 + (1/2)*m*v^2 = 14.41 + 0.5*7.5*3.1^2 = 14.41 + 36.04 = 50.45 J

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