I am stuck on this problem and cannot figure it out for the life of me. Please b

Question

I am stuck on this problem and cannot figure it out for the life of me. Please break it down for me... I dont see how I get a force to even get work from the givens in this equation... "A CD player rotates at a variable speed so that a laser can scan pits and land on the disk's bottom surface at a constant tangential speed of 1.2 m/s. The disk has a moment of inertia of 1.2x10^-4 kg m^2 and the music is first detected when the laser is located 15 mm from the disk's center. Assuming the disk starts from rest, find the work done by the motor during this start-up"

Explanation / Answer

Since this is a rotational motion problem, you don't necessarily want to get energy from work. Instead, you want to work with parameters such as torque, angular velocity, angular acceleration, and moment of inertia. It is, otherwise, exactly the same as any work-energy problem.

What this problem is basically asking is what is the work required to spin the CD such at the tangential velocity is 1.2 m/s at 15 mm from the center. From conservation of energy, the work done by the motor should equal the rotational kinetic energy of the disc at that point:

W = KE = (1/2)*I*2

I is already given (1.2x10^-4 kg m^2), so we just need to figure out , angular velocity.

The formula to convert between tangential and angular velocity is

v = r

where r is the distance from the center and v is the tangential velocity. In this case, r = 15 mm, so

= v/r = (1.2m/s)/(15x10^-3 m) = 80 rad/s

Now plug in and I back into the W=KE formula and you should be able to calculate work.

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