A computer is reading data from a rotating CD-ROM. At a point that is 0.032 m from the center of the disc, the centripetal acceleration is 111 m/s2. What is the centripetal acceleration at a point that is 0.070 m from the center of the disc?
To find the centripetal acceleration at a point that is 0.070 m from the center of the disc, we can use the formula for centripetal acceleration:
a = (v^2) / r
Where:
a is the centripetal acceleration
v is the linear velocity of the object
r is the distance from the center of rotation
Given that the centripetal acceleration at a point 0.032 m from the center is 111 m/s², we need to find the linear velocity at that point in order to calculate the centripetal acceleration at a distance of 0.070 m from the center.
First, let's find the linear velocity at the point 0.032 m from the center. We can use the centripetal acceleration formula in this case:
a = (v^2) / r
Rearranging the formula to solve for v:
v = sqrt(a * r)
Substituting the given values:
v = sqrt(111 m/s² * 0.032 m) = 0.607 m/s
Now that we have the linear velocity at that point, we can use it to find the centripetal acceleration at a distance of 0.070 m from the center:
a = (v^2) / r
Substituting the values:
a = (0.607 m/s)^2 / 0.070 m
a = 0.369 m/s²
Therefore, the centripetal acceleration at a point that is 0.070 m from the center of the disc is approximately 0.369 m/s².