To determine the number of revolutions per minute the sample is making, we need to find the angular velocity of the sample first.
We know that the centripetal acceleration (ac) of the sample is 6.60x10^3 times as large as the acceleration due to gravity (g). Mathematically, we can express this as:
ac = 6.60 x 10^3 * g
The centripetal acceleration is given by the formula:
ac = ω^2 * r
Where:
ω is the angular velocity (in radians per second)
r is the radius of rotation (in meters)
We are given the radius of rotation as 4.28 cm, which we convert to meters:
r = 4.28 cm = 0.0428 m
Substituting the values into the formula, we get:
6.60 x 10^3 * g = ω^2 * 0.0428
Next, we rearrange the equation to solve for ω:
ω = √(6.60 x 10^3 * g / 0.0428)
To find the number of revolutions per minute, we need to convert the angular velocity from radians per second to revolutions per minute.
1 revolution = 2Ï€ radians
1 minute = 60 seconds
So, to convert from radians per second (ω) to revolutions per minute (rpm), we use the following conversion factor:
1 rpm = (1 revolution / 2Ï€ radians) * (60 seconds / 1 minute)
Finally, we substitute the value of ω and simplify the expression to find the number of revolutions per minute.