The hard disk in a laptop computer contains a small disk that rotates at a rate of 5000 rpm. If this disk has a radius of 2.3 cm, what is the centripetal acceleration of a point at the edge of the disk?_____m/s^2

n= 5000 rpm =83.33 rev/s

ω=2πn=2•π•83.33=523.6 rad/s.
a(centr) = ω²R=523.6²•0.023=6305.6 m/s²

Centripetal acceleration (ac) is given by the equation:

ac = (ω^2) * r

where ω is the angular velocity in radians per second, and r is the radius.

First, we need to convert the rotational speed from revolutions per minute (rpm) to radians per second (rad/s):

ω = (5000 rpm) * (2π rad/1 min) * (1 min/60 s)
= (5000 * 2π) / 60
≈ 523.6 rad/s

Next, we can substitute the values into the centripetal acceleration formula:

ac = (523.6 rad/s)^2 * 0.023 m
≈ 1446.6 m/s^2

Therefore, the centripetal acceleration of a point at the edge of the disk is approximately 1446.6 m/s^2.

To calculate the centripetal acceleration (a) of a point at the edge of a spinning disk, we can use the formula:

a = (v^2) / r

Where:
v = tangential velocity
r = radius of the disk

In this case, the tangential velocity (v) can be determined using the rotational rate (angular velocity) of the disk. The angular velocity (ω) is given in revolutions per minute (rpm), but we need it in radians per second (rad/s) for consistent units.

1 revolution = 2π radians

So, the angular velocity can be calculated as:

ω = (5000 rpm) * (2π rad/1 min) * (1 min/60 s)

Plugging in the given values and performing the calculation:

ω = (5000 rpm) * (2π rad/1 min) * (1 min/60 s)
ω = (5000 * 2π) / 60 rad/s
ω ≈ 523.6 rad/s (rounded to one decimal place)

Now, we can calculate the tangential velocity (v) using the formula:

v = ω * r

Plugging in the values:

v = (523.6 rad/s) * (2.3 cm)
v ≈ 1201.9 cm/s (rounded to one decimal place)

Finally, we can substitute the values of v and r into the centripetal acceleration formula:

a = (v^2) / r

a = (1201.9 cm/s)^2 / (2.3 cm)
a ≈ 618940.4 cm^2/s^2 (rounded to one decimal place)

Converting cm^2/s^2 to m/s^2:

1 m = 100 cm

So,

a ≈ 6189.4 m/s^2 (rounded to one decimal place)

Therefore, the centripetal acceleration of a point at the edge of the disk is approximately 6189.4 m/s^2.

To calculate the centripetal acceleration of a point at the edge of the disk, we can use the formula for centripetal acceleration:

a = (v^2) / r

where:
a is the centripetal acceleration,
v is the linear velocity,
r is the radius of the disk.

To find the linear velocity (v) at the edge of the disk, we can use the formula:

v = (2 * π * r * n) / 60

where:
r is the radius of the disk,
n is the rotational speed in revolutions per minute (rpm).

First, let's convert the rotational speed from rpm to revolutions per second (rps):

n = 5000 rpm / 60 seconds = 83.33 rps (rounded to two decimal places)

Now, we'll substitute the values in the linear velocity formula:

v = (2 * π * 2.3 cm * 83.33 rps) / 60

The radius of 2.3 cm should be converted to meters before performing the calculation:

v = (2 * π * 0.023 m * 83.33 rps) / 60

v ≈ 7.667 m/s

Now, we can substitute this velocity value into the centripetal acceleration formula:

a = (7.667 m/s)^2 / 0.023 m

a ≈ 2597.682 m/s^2 (rounded to three decimal places)

Therefore, the centripetal acceleration of a point at the edge of the disk is approximately 2597.682 m/s^2.