If a rotating disk starts from rest and ends up at 200 rpm in 4 seconds, what is the angular acceleration? How many revolutions occur during the process?
If that same disk, after the power is turned off comes to rest in 20 seconds, what is the angular deceleration?
O darn i meant to change my name to Tobias. this is a physics question
no one is answer it anyway what
Hey tobias
To find the angular acceleration, we can use the formula:
Angular acceleration (α) = (Final angular velocity (ω) - Initial angular velocity (ω₀)) / time (t)
Given:
Initial angular velocity (ω₀) = 0 (since the disk starts from rest)
Final angular velocity (ω) = 200 rpm = (200/60) rad/s = 20/3 rad/s
Time (t) = 4 seconds
Plugging in the values, we get:
Angular acceleration (α) = (20/3 - 0) / 4
= (20/3) / 4
= 20/12
= 5/3 rad/s²
Therefore, the angular acceleration is 5/3 rad/s².
To find the number of revolutions that occur during the process, we can use the formula:
Number of revolutions = Final angular displacement / (2π)
Since the disk starts from rest, the initial angular displacement is 0. The final angular displacement can be found using the formula:
Angular displacement (θ) = (Initial angular velocity + Final angular velocity) / 2 * time
Plugging in the values, we get:
Angular displacement (θ) = (0 + (20/3)) / 2 * 4
= (20/3) / 2 * 4
= (20/3) / 8
= 20/24
= 5/6 rad
Number of revolutions = (5/6) / (2π)
= (5/6) / (2 * 3.14)
≈ 0.13 revolutions
Therefore, approximately 0.13 revolutions occur during the process.
Now, for the deceleration:
To find the angular deceleration, we can use the formula:
Angular deceleration (α) = (Final angular velocity (ω) - Initial angular velocity (ω₀)) / time (t)
Given:
Initial angular velocity (ω₀) = 200 rpm = (200/60) rad/s = 20/3 rad/s
Final angular velocity (ω) = 0 (since the disk comes to rest)
Time (t) = 20 seconds
Plugging in the values, we get:
Angular deceleration (α) = (0 - (20/3)) / 20
= -(20/3) / 20
= -20/60
= -1/3 rad/s²
Therefore, the angular deceleration is -1/3 rad/s².