Answer: 0.4299s.
Explanation: To find the angular acceleration ,Newton's second angular law will be used.
τ = I α
Wr = I α
The weight is applied in the middle of the pencil , sin 10 = r / (L/2).
r = L/2 sin 10
the moment of inertia will be: I = 1/3 M L²
mg L / 2 sin 10 = (1/3 m L²) α
αf = 3/2 g / L sin 10
α = [3/2 × 9.8] / [0.150 sin10]
α = 17 rad/s²
angle from the vertical to the ground θ = π / 2
t = √ (2 π / (2 α ))
t = √(π / α )
t = √(π / 17)
t = √3.142 / 17
t = 0.4299s
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