The plastic in a DVD disk will begin to deform at rotations faster than 10,000 revolutions per minute.
How many radians per second is that?
If the disk has a radius of 0.06 m, what is the centripetal acceleration at the edge?
To convert rpm to rad/s, multiply by
(2 pi rad/rev)*(1 min/60 s)
The Greek symbol omega (usually typed as w here) is usually used for rotation rates in radians per second.
Centripetal acceleration is R*w^2, where R is the radius.
You can do the numbers, I'm sure.
got it. thanks
To find the number of radians per second, we need to convert revolutions per minute to radians per second.
1 revolution = 2π radians
1 minute = 60 seconds
First, we convert revolutions per minute to revolutions per second by dividing by 60:
10,000 revolutions/minute = 10,000/60 revolutions/second
Next, we convert revolutions to radians by multiplying by 2π:
10,000/60 revolutions/second * 2π radians/revolution
Simplifying the expression gives us:
(10,000 * 2π)/60 radians/second
Now we can calculate the value:
(10,000 * 2π)/60 = 10,000π/60 radians/second ≈ 523.6 radians/second
Therefore, rotating at 10,000 revolutions per minute is approximately equal to 523.6 radians per second.
To find the centripetal acceleration at the edge of the disk, we can use the formula for centripetal acceleration:
Centripetal acceleration = (angular velocity)^2 * radius
Given that the radius of the disk is 0.06 m and the angular velocity is 523.6 radians/second (from the previous calculation), we can substitute these values into the formula:
Centripetal acceleration = (523.6 radians/second)^2 * 0.06 m
Calculating this expression gives us:
Centripetal acceleration ≈ (523.6^2) * 0.06 ≈ 172,779.136 m/s^2
Therefore, the centripetal acceleration at the edge of the disk is approximately 172,779.136 m/s^2.