Circular and Satellite Motion Legacy Problem #5 Guided Solution
Problem*
A manufacturer of CD-ROM drives claims that the player can spin the disc as frequently as 1200 revolutions per minute.
- If spinning at this rate, what is the speed of the outer row of data on the disc; this row is located 5.6 cm from the center of the disc?
- What is the acceleration of the outer row of data?
Audio Guided Solution
A good problem solver reads the problem carefully, identifies the known quantities and the unknown quantities, and uses physics concepts and conceptual reasoning to get from the givens to the unknown quantities. Here we read about a CD-ROM, and particularly the outer row of data on the CD-ROM disc that is moving in a circle. We're told that it revolves 1,200 revolutions per minute. That is in a time of 60 seconds, this outer row of the CD makes 1,200 complete circumferences or circles. We're asked two things, first to determine the speed of this outer row of data, and second to determine the acceleration. We're told the outer row is 5.6 centimeters from the center of the disc. In order to determine the speed, we have to do a distance to time ratio. The distance we'll take is the distance for 1,200 revolutions, and the time we'll take is 60 seconds. If we do the problem in centimeters per second, we will do the distance is 1,200 times 2 times pi times 5.6 centimeters. We'll divide this by 60 seconds, and that will get us a speed of 703.7 centimeters per second. Converting to meters per second, it becomes 7.037 meters per second. Now to get the acceleration, we have to take the speed squared and divide it by the radius. We'll take the same speed of 703.7 centimeters per second and square it, and then divide by 5.6 centimeters. That gives us an acceleration of 88,431.6 centimeters per second per second, or in meters per second, it would be 8.84 times 10 to the second meters per second per second.
Solution
- 7.0 x 102 cm/s or 7.0 m/s
- 8.8 x 104 cm/s/s or 8.8 x 102 m/s/s
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(\descriptive{m}{m,mass} = 61.7\unit{kg}\), \(\descriptive{v}{v,velocity} = 18.5 \unit{\meter\per\second}\), \(\descriptive{R}{R,radius} = 30.9\unit{m}\), \(F_\text{norm} = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
Read About It!
Get more information on the topic of Circular and Satellite Motion at The Physics Classroom Tutorial.