# Question 7.4: TRACK LENGHT OF A COMPACT DISC GOAL Relate angular to linear...

**TRACK LENGHT OF A COMPACT DISC**

**GOAL** Relate angular to linear variables.

**PROBLEM** In a compact disc player, as the read head moves out from the center of the disc, the angular speed of the disc changes so that the linear speed at the position of the head remains at a constant value of about 1.3 m/s. (**a**) Find the angular speed of a CD of radius 6.00 cm when the read head is at r = 2.0 cm and again at r = 5.6 cm. (**b**) An old-fashioned record player rotates at a constant angular speed, so the linear speed of the record groove moving under the detector (the stylus) changes. Find the linear speed of a 45.0-rpm record at points 2.0 cm and 5.6 cm from the center. (**c**) In both the CDs and phonograph records, information is recorded in a continuous spiral track. Calculate the total length of the track for a CD designed to play for 1.0 h.

**STRATEGY** This problem is just a matter of substituting numbers into the appropriate equations. Part (**a**) requires relating angular and linear speed with Equation 7.10, v_t = rω, solving for ω, and substituting given values. In part (**b**), convert from rev/min to rad/s and substitute straight into Equation 7.10 to obtain the linear speeds. In part (**c**), linear speed multiplied by time gives the total distance.

**"Step-by-Step Explanation"**refers to a detailed and sequential breakdown of the solution or reasoning behind the answer. This comprehensive explanation walks through each step of the answer, offering you clarity and understanding.

Our explanations are based on the best information we have, but they may not always be right or fit every situation.

**blue check mark**means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.

Learn more on how we answer questions.