Answer:
ωf = 25.9 rad/s
Explanation:
The uniformly accelerated circular movement, is a circular path movement in which the angular acceleration is constant.
We apply the equations of circular motion uniformly accelerated
θ= ω₀*t + (1/2)*α*t² Formula (1)
ωf= ω₀ + α*t Formula (2)
Where:
θ : angle that the body has rotated in a given time interval (rad)
α : angular acceleration (rad/s²)
t : time interval (s)
ω₀ : initial angular speed ( rad/s)
ωf : final angular speed ( rad/s)
Data
α= 5.40 rad/s2
θ= 60.4 rad
t = 4.00 s
Calculating of the initial angular speed of the spinning axle:
We replace data in the formula (1):
θ= ω₀*t + (1/2)*α*t²
60.4= ω₀*(4) + (1/2)*(5.4)(4)²
60.4= ω₀*(4) + 43.2
60.4 - 43.2= ω₀*(4)
17.2 = ω₀*(4)
ω₀ = 17.2 /4
ω₀ = 4.3 rad/s
Calculating of the final angular speed of the spinning axle:
We replace data in the formula (2):
ωf = ω₀ + α*t
ωf = 4.3 + (5.4)(4)
ωf = 25.9 rad/s
