A computer is reading data from a rotating CD-ROM. At a point that is 0.0382 m from the center of the disk, the centripetal acceleration is 118 m/s2. What is the centripetal acceleration at a point that is 0.0791 m from the center of the disc?
centripetal acceleration=I w^2 r so it is dependent linearly on R.
Acceleartion=118m/s^2 * (.0791/.0382)
To find the centripetal acceleration at a point that is 0.0791 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, and r is the radius.
To find the linear velocity at the first point (0.0382 m from the center), we need to consider that the angular velocity is constant throughout the disc. The linear velocity is given by the formula:
v = ω * r
where ω is the angular velocity.
Since the angular velocity is constant, and the distance from the center is different, we can set up a proportion:
v1 / r1 = v2 / r2
where v1 is the linear velocity at the first point, r1 is the radius at the first point, v2 is the linear velocity at the second point, and r2 is the radius at the second point.
We plug in the given values:
v1 / 0.0382 = v2 / 0.0791
Now, we can solve for v2, the linear velocity at the second point:
v2 = (v1 * 0.0791) / 0.0382
Next, we can substitute the value of v2 into the formula for centripetal acceleration:
a2 = (v2^2) / r2
a2 = ((v1 * 0.0791) / 0.0382)^2 / 0.0791
Now, we can plug in the given values for v1 and solve for a2:
a2 = ((118 * 0.0791) / 0.0382)^2 / 0.0791
Calculating this expression gives us the centripetal acceleration at a point that is 0.0791 m from the center of the disc.