A centrifuge in a medical laboratory rotates at an angular speed of 3500 rev/ min. When switched off, it rotates through 41.0 revolutions before coming to rest. (a) Find the angular speed in rad/s. (b) Find the displacement in radians. (c) Find the constant angular acceleration of the centrifuge.
a. Do that, 1rev=2PI radians, 1min=60sec
b.
displaement=2PI*revolutions
c. Wf^2=Wi^2+2 a d find a.
To find the answers to these questions, we need to use the formulas related to angular speed, angular displacement, and angular acceleration.
(a) To find the angular speed in rad/s, we can convert the given angular speed from revolutions per minute (rev/min) to radians per second (rad/s). The conversion factor is 1 rev = 2π rad. So, we can use the following formula:
Angular speed (rad/s) = Angular speed (rev/min) * 2π / 60
Substituting the given value:
Angular speed (rad/s) = 3500 rev/min * 2π / 60
Now, let's calculate the result.
(b) To find the displacement in radians, we can use the formula:
Angular displacement (radians) = Number of revolutions * 2π
In the given problem, it is mentioned that the centrifuge rotates through 41.0 revolutions before coming to rest. So, the angular displacement can be calculated as follows:
Angular displacement (radians) = 41.0 revolutions * 2π
Now, let's calculate the result.
(c) To find the constant angular acceleration of the centrifuge, we use the formula for angular acceleration:
Angular acceleration (rad/s²) = (Final angular speed - Initial angular speed) / Time taken
Since the centrifuge comes to rest, its final angular speed is 0 rad/s. The initial angular speed can be obtained using the angular displacement and time taken:
Initial angular speed (rad/s) = Angular displacement (radians) / Time taken
Substituting the given values, we can calculate the initial angular speed. Then, using the formula, we can calculate the angular acceleration.
Now, let's calculate the result.
By following these steps and using the formulas, we can find the answers to all three parts of the question.