A computer is reading data from a rotating CD-ROM. At a point that is 0.036 m from the center of the disc, the centripetal acceleration is 120 m/s2. What is the centripetal acceleration at a point that is 0.056 m from the center of the disc?
To find the centripetal acceleration at a point that is 0.056 m from the center of the disc, we can use the formula for centripetal acceleration:
ac = (v^2) / r
Where:
- ac is the centripetal acceleration
- v is the linear speed of the object
- r is the radius from the center of the circular path
In this case, we are given the centripetal acceleration at a point 0.036 m from the center (ac1 = 120 m/s^2). We need to find the centripetal acceleration at a point 0.056 m from the center (ac2).
Since the linear speed (v) remains the same for a given rotating disk, we can set up the equation:
ac1 = ac2
(v^2) / r1 = (v^2) / r2
Since the v^2 cancels out, the equation becomes:
r2 = (r1 * ac1) / ac2
Substituting the given values, we get:
r2 = (0.036 m * 120 m/s^2) / ac2
Now we can solve for ac2 by rearranging the equation:
ac2 = (0.036 m * 120 m/s^2) / r2
Plug in the value of r2 (which is 0.056 m):
ac2 = (0.036 m * 120 m/s^2) / 0.056 m
Now we can calculate the centripetal acceleration at the given point:
ac2 = 77.14 m/s^2
Therefore, the centripetal acceleration at a point that is 0.056 m from the center of the disc is approximately 77.14 m/s^2.