Awheel is turning about an axis through its center with constant angular acceleration. starting from rest, at t = 0, the wheel turns through 8.20 revolutions in 12.0 s. at t = 12.0 s the kinetic energy of the wheel is 36.0 j. for an axis through its center, what is the moment of inertia of the wheel?

I=0.489 kg.m²

Explanation:

Given that

Initial speed of wheel (ω₁)= 0 rad/s

θ = 8.2 rev in t= 12 s

We know that

1 rev = 2π rad

8.2 rev = 16.4 π rad

θ =16.4 π rad

Lets take angular acceleration of wheel is α rad/s²

We know that if angular acceleration is constant

Now by putting the values

α =0.715 rad/s²

The final speed of the wheel at 12 s

ω₂=ω₁ + α  t

ω₂ = 0 + 0.715 x 12

ω₂ =8.58 rad/s

The final kinetic energy of the wheel

I=0.489 kg.m²

This is moment of inertia of the wheel .

u=13

v=30

s/t=u+1\2at

=13+431/2

=13+265.5

=278.5