Respuesta :
Answer:
a = -210,066 rad/s2
Explanation:
The rotation speed of the centrifuge is 3400 revolutions/min. Converting this to rev/sec, we divide by 60, so 56.666 rev/sec
when switched off, it rotated 48 revolutions before stopping. using the Torricelli formula, we can find the acceleration it took to stop:
V2 = Vo2 + 2*a*DS, where:
V = 0
Vo = 56.666
DS = 48
Then, applying these values in the formula, we have:
0 = 3211.111 + 2*a*48
a = -3211.111/96 = -33.45 rev/s2
to convert from revolution to rad, we can multiply by 2*pi (1 revolution = 2pi rad)
a = -33.45 * 2 * pi = -210,066 rad/s2
Given Information:
Initial angular speed = ωi = 3,400 rev/min = 56.67 rev/sec
Angular displacement = ΔΘ = 48 revolutions
Required Information:
Angular acceleration = α = ?
Answer:
Angular acceleration = -209.41 rad/s²
Explanation:
We know from the kinematics,
2aS = Vf² - Vi²
This equation can be written in terms of rotational motion as
2αΔΘ = ωf² - ωi²
α = (ωf² - ωi²)/2ΔΘ
Where the final angular speed ωf² is zero since it was switch off.
α = (0 - (56.67)²)/2*48
α = (0 - (56.67)²)/2*48
α = -33.33 rev/s²
Since 1 revolution is equal to 2π radians
α = -33.33*2π
α = -209.41 rad/s²
The negative sign indicates deceleration.
Therefore, the constant angular acceleration of the centrifuge is 209.41 rad/s².
