Suppose a circular platform is rotating at a constant rate of 24 rev/min. How far away from the centre would one need to stand in order to have an radial acceleration of 9.9 m/s2? Express your answer in cm.
To solve this problem, we can use the formula for radial acceleration:
ar = rω^2
Where:
ar is the radial acceleration,
r is the distance from the center, and
ω is the angular velocity.
First, let's convert the given angular velocity from rev/min to rad/s:
ω = (24 rev/min) x (2π rad/rev) x (1 min/60 s)
ω = 24 x 2π / 60 rad/s
ω = π / 5 rad/s
Now, we can plug the values into the formula and solve for r:
9.9 m/s^2 = r * (π / 5)^2
Simplifying the equation:
9.9 m/s^2 = r * (π^2) / 25
To find r, we need to rearrange the equation:
r = (9.9 m/s^2 * 25) / (π^2)
r ≈ 3.16 m
Finally, we need to convert the answer from meters to centimeters:
r = 3.16 m x (100 cm/1 m)
r ≈ 316 cm
Therefore, you would need to stand approximately 316 cm away from the center to have a radial acceleration of 9.9 m/s^2.