Compact Disc. A compact disc (CD) stores music in a coded pattern of tiny pits 10^-7 m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.25 m/s. (a) What is the angular speed of the CD when the innermost part of the track is scanned? The outermost part of the track?

Video transcript

Welcome back, everyone. We are making observations about a circular table top. You're told that has a radius of 1 m and we wish to print a spiral decoration whose radius increases outward by spinning the top. Now, the printing head will have a constant linear printing speed of 50 millimeters per second or 0.05 m per second. And it starts at an at a point that gives an inner radius of 0.1 m and it ends at a point that gives a radius of 0.9 m. And we are tasked with finding what is the angular velocity at the inner radius and what is the angular velocity at the outer radius? Let's take a look at our answer choices here. Answer choice A is that our inner radius, angular velocity is 500 radiant per second for the outer, it's 55.6 radiant per second. Answer. Choice B has our inner being two radiant per second and our outer being 17.9 radiant per second. Answer. Choice C has our in inner angular velocity being 0.5 radiant per second and our outer being 0.056 radiant per second. An answer choice D has our inner angular velocity of 0.0050 radiant per second and our outer of 0.045 radiance per second. What do we do here? Well, for both of these, we are going to use a very similar formula here. And it's just simply the tangential velocity or our printer head velocity divided by the radius at that point before our inner angular velocity. It'll simply just be 0.05 divided by 0.1 giving us 0.5 radiance per second for our inner angular velocity or our outer very similar. Except this time, we're gonna be dividing by our outer radius which gives us 0.05 divided by 0.9 giving us 0.056 radiance per second. Now, we have found both the inner angular velocity and the outer angular velocity corresponding to our final answer. Choice of c Thank you all so much for watching. I hope this video helped. We will see you all in the next one.