A computer is reading data from a rotating CD-ROM. At a point that is 0.0368 m from the center of the disk, the centripetal acceleration is 274 m/s2. What is the centripetal acceleration at a point that is 0.0781 m from the center of the disc?
The centripetal acceleration is proportional to the distance from the center, since the angular velocity w is the same everywhere on the disc. .
(0.0781/0.0368) x 274 = _____ m/s^2
To find the centripetal acceleration at a point that is 0.0781 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 distance from the center of the disc.
Given that the centripetal acceleration at a point 0.0368 m from the center of the disc is 274 m/s^2, we can calculate the linear velocity at that point.
Let's calculate it step by step:
Step 1: Calculate the linear velocity at the point 0.0368 m from the center.
a = (v^2) / r
274 = (v^2) / 0.0368
Rearranging the equation:
v^2 = 274 * 0.0368
v^2 = 10.0912
v = √10.0912
v ≈ 3.18 m/s
Step 2: Calculate the centripetal acceleration at the point 0.0781 m from the center.
Now, using the linear velocity we just found, let's substitute it into the formula.
a = (v^2) / r
a = (3.18^2) / 0.0781
a = 10.1124 / 0.0781
a ≈ 129.48 m/s^2
Therefore, the centripetal acceleration at a point that is 0.0781 m from the center of the disc is approximately 129.48 m/s^2.
To find the centripetal acceleration at a point that is 0.0781 m from the center of the disc, we can use the formula for centripetal acceleration:
ac = ω^2 * r
where ac is the centripetal acceleration, ω is the angular velocity, and r is the radius.
In this case, we are given the centripetal acceleration at a point 0.0368 m from the center, which is 274 m/s^2. Let's call this ac1 and r1. We can substitute these values into the formula:
ac1 = ω^2 * r1
Solving for ω, we have:
ω^2 = ac1 / r1
ω = √(ac1 / r1)
Now, let's find the angular velocity ω using the given values.
ω = √(274 m/s^2 / 0.0368 m)
ω ≈ 61.92 rad/s
Now that we have the angular velocity, we can find the centripetal acceleration at a point 0.0781 m from the center. Let's call this ac2 and r2. We can use the formula:
ac2 = ω^2 * r2
Substituting the known values:
ac2 = (61.92 rad/s)^2 * 0.0781 m
ac2 ≈ 298.93 m/s^2
Therefore, the centripetal acceleration at a point that is 0.0781 m from the center of the disc is approximately 298.93 m/s^2.