the tub of a washing machine is initially at rest. when the spin cycle begins, it begins to rotate. In the first 2.80 s, it makes 3 complete revolutions. what is its final angular velocity?
velocity increases linearly from 0 to final so average angular velocity is half the final
average angular velocity = 3*2 pi radians / 2.8 seconds
so
final = (12 pi/2.8) radians/second
algebra why it works :)
v = a t
final V = a T where T is final t
d = (1/2) a t^2
final D = (1/2) V/T * T^2 = (1/2) V T
To find the final angular velocity of the tub, we can use the formula:
Angular velocity (ω) = (2π * Number of revolutions) / Time
Given:
Number of revolutions = 3
Time = 2.80 s
Substituting the values into the formula:
ω = (2π * 3) / 2.80
Calculating:
ω = 6π / 2.80
Approximating the value of π as 3.14:
ω ≈ 6 * 3.14 / 2.80
ω ≈ 18.84 / 2.80
ω ≈ 6.72
Therefore, the final angular velocity of the tub is approximately 6.72 rad/s.
To find the final angular velocity of the tub, we can use the definition of angular velocity, which is the change in angle divided by the change in time.
Given that the tub makes 3 complete revolutions in 2.80 seconds, we can find the change in angle by multiplying the number of revolutions by 360 degrees (since there are 360 degrees in a full revolution). Therefore, the change in angle is:
Change in angle = 3 revolutions * 360 degrees/revolution = 1080 degrees
Next, we need to convert the change in angle from degrees to radians, because angular velocity is typically measured in radians per second. Since there are 2π radians in a full circle (360 degrees), we can convert degrees to radians using the following conversion factor:
1 degree = π/180 radians
Hence, the change in angle in radians is:
Change in angle (in radians) = 1080 degrees * (π/180 radians/degree) ≈ 18.85 radians
Finally, we can calculate the final angular velocity using the formula:
Angular velocity = Change in angle / Change in time
Angular velocity = 18.85 radians / 2.80 seconds ≈ 6.73 radians per second
Therefore, the final angular velocity of the tub is approximately 6.73 radians per second.