Answer:
a) τ = 421.9 N m, b) F = 168.76 N
Explanation:
For this exercise we use Newton's second law for rotational motion
τ = I α
Let's find the angular acceleration with kinematics
w = w₀ + α t
as part of rest its initial angular velocity is zero wo = 0
α= w / t
let's reduce the magnitudes to the SI system
w = 15 rpm (2π rad / 1 rev) (1 min / 60s) = 1.57 rad / s
let's calculate
α = 1.57 /10
α = 0.157 rad / s²
Now let's look for the moment of inertia, which is the sum of the moment of inertia of the disk plus the moment of the children
disk moment I₁ = ½ M r²
moment of each child I₂ = m r²
I = I₁ + 2 I₂
I = ½ M r² + 2 m r²
we substitute
τ = (½ M r2 + 2 m r2) alpha
τ = r² (½ M + 2 m) α
τ = 2.5² (760/2 + 2 25) 0.157
τ = 421.9 Nm
What force is applied
τ = F r
F = τ / r
F = 421.9 / 2.5
F = 168.76 N
