The angular velocity of the wheel after its mass center G has traveled through a distance starting from rests is 31.62 m.
The velocity of an object when moving on a circular track.
The moment of inertia of the wheel about the center O is
I = mk²
Where radius of gyration k= 300mm =0.3 m and mass of wheel m =30kg
I = 20 x (0.3)² = 1.8 kg.m²
The final kinetic energy of wheel is
K.Ef = 1/2 x mx (rω²) + 1/2 x I x ω²
Substitute the values from the question, we have
K.Ef = 1/2 x 20 x (0.4 x ω²) +1/2 x 1.8 x ω² =2.5ω²
The initial kinetic energy is zero, K.Ei =0
According to the work energy theorem, W =K.Ef -K.Ei =2.5ω² ...............(1)
Work done = moment x angular displacement
W = 50 N.m x 20m/0.4m = 2500 N.m............(2)
Equating both the equations and solving for ω, we get
ω =31.62 rad
Thus, the angular velocity is 31.62 rad.
Learn more about angular velocity.
https://brainly.com/question/13649539
#SPJ1
