Respuesta :
The angular acceleration of the grindstone is 0.199 rad / s²and the number of turns, N, that the stone will make before coming to rest is 36.94 rev.
(a)To solve this, we will use Newton's second law for rotational movement, i.e. torque
τ = I α
⇒ f × r = I × α
Now we write the translational Newton equation in the radial direction
N- F = 0
⇒N = F
The friction force equation is
f = μ N
⇒ f = μ F
The moment of inertia is
I = ½ m r²
Let's replace in the torque equation
(μ F) r = (½ m r²) α
α = 2 μ F / (m r)
α = 2 (0.2)15/ (91 × 0.33)
α = 0.199 rad / s²
b) Using the relationship of rotational kinematics
w² = w₀² - 2 α θ
0 = w₀² - 2 α θ
θ = w₀² / 2 α
Reducing the angular velocity,
w₀ = 92 rpm (2π rad / 1 rev) (1 min / 60s) = 9.634 rad / s
θ = (9.634)² / (2 × 0.199)
θ = 232 rad
Reducing radians to revolutions
θ = 232 rad (1 rev / 2π rad)
θ = 36.94 rev
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