Starting from rest, a wheel with constant angular acceleration turns through an angle of 25 rad in a time t. What will its angular velocity be after 3t?

θ = 225 rad

Explanation:

given data

angle = 25 rad

to find out

angular velocity after 3t?

solution

let angular acceleration α in t

θ = ω × t + 0.5 × α × t²        1

here ω  = 0 (initial velocity )

so put this value here

25 = 0 + 0.5 × α × t²             2

α = 25 ÷ (0.5 t²)

α = 50 ÷ t²                            3

now here we take in 3t

θ = ω × 3t + 0.5 × α × (3t)²

for ω  = 0

θ = 0 + 0.5 × α × 9t²

now put value in eq 2

so

θ = (0.5) ×  (50 ÷ t²) ×  (3t)²

θ = 25 × 9

θ = 225 rad

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