The time after it starts spinning, that the box will slip off is 0.1 s.
<h3>Apply the principle of conservation of angular momentum</h3>
I₁ω₁ - I₂ω₂ = 0
I₁ω₁ = I₂ω₂
where;
- I₁ is initial moment of inertia
- I₂ is final moment of inertia
- ω₁ is initial angular speed
- ω₂ is final angular speed
The final angular speed when the box slides off;
ω₂ = I₁ω₁ / I₂
ω₂ = [0.5(m₁ + m₂)(R + r)²] / (0.5MR²)
ω₂ = [0.5(30 + 0.3)(3.1 + 1.4)²] / (0.5 x 30 x 3.1²)
ω₂ = 2.13 rad/s
Time taken for the for box to slide off;
τ = Iα
τ = I(ω/t)
τ = (Iω)/t
t = (Iω)/τ
t = (0.5 x 0.3 x 1.4² x 2.13)/6
t = 0.1 s
Thus, the time after it starts spinning, that the box will slip off is 0.1 s.
Learn more about moment of inertia here: brainly.com/question/3406242
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