A centrifuge accelerates uniformly from rest to 18000 rpm in 180 s. Through how many revolutions did it turn in this time?
To calculate the number of revolutions, we need to convert the angular velocity from rpm to revolutions per second. The formula to convert from rpm to revolutions per second is:
Revolutions per second = rpm / 60
Given that the centrifuge accelerated uniformly from rest to 18000 rpm in 180 seconds, we can use this information to find the number of revolutions.
Step 1: Convert angular velocity from rpm to revolutions per second.
18000 rpm / 60 = 300 revolutions per second.
Step 2: Use the formula for uniformly accelerated motion to find the number of revolutions.
The formula to calculate the number of revolutions is:
Number of revolutions = (Initial angular velocity * Time) + (1/2 * Angular acceleration * Time^2)
Since the centrifuge starts from rest, the initial angular velocity is 0. The angular acceleration can be calculated using the formula:
Angular acceleration = Final angular velocity / Time
Step 3: Calculate the angular acceleration.
Angular acceleration = 18000 rpm / 180 s = 100 revolutions per second squared.
Step 4: Calculate the number of revolutions using the formula.
Number of revolutions = (0 * 180) + (1/2 * 100 * 180^2)
Number of revolutions = 0 + 1/2 * 100 * 32400
Number of revolutions = 0 + 1/2 * 3240000
Number of revolutions = 1620000
Therefore, the centrifuge turned 1,620,000 revolutions in 180 seconds.
d=wi*t+1/2 a t^2
revolutions= 0+1/2 (18000rpm/180)180^2
or you could have used
revolutions= avg veloicty*time