Answer:
ω = 2.13rad/s
Explanation:
Given
F = 1N = force applied, m = 16kg, R = 0.2m
ωo = 1.2rad/s
t = 1.5s
ω = ?
Where
α = angular acceleration
ωo = initial angular speed
And ω = angular speed at a later time t
For a rigid body rotating about an axis
τ = FR= I×α
I = 1/2×MR² for a uniform disk
FR = (1/2×mR²)×α
= 1/2×mR²×(ω – ωo)/t
Therefore
FR= 1/2×mR²×(ω – ωo)/t
2Ft/mR = ω – ωo
ω = 2Ft/mR + ωo
ω = 2×1×1.5/(16×0.2) + 1.2 = 2.13 rad/s
Newton's second law and kinematics for rotational motion allows to find the result for the angular velocity of the disk is:
w = 1.24 rad / s
Given parameters
To find
Newton's second law for rotational motion stable a relationship between torque, moment of inertia, and angular acceleration.
τ = I α
where I is the moemnt inerti and α is the angular acceleration.
The moment of inertia of a disk is tabulated.
I = ½ m r²
Torque is the product of the force times the arm or perpendicular distance
τ = F r
Let's substitute
F r = (½ m r²) α
α = [tex]\frac{2 F r}{m}[/tex]
Let's calculate
α = [tex]\frac{2 \ 1 \ 0.2 }{16}[/tex]
α = 0.025 rad / s²
Rotational kinematics studies the rotational motion of bodies, let's use the relation
w = w₀ + α t
Let's calculate
w = 1.2 + 0.025 1.5
w = 1.2375 rad / s
w = 1.24 rad / s
In conclusion using Newton's second law and kinematics for rotational motion we can find the result for the angular velocity of the disk is:
w = 1.24 rad / s
Learn more here: brainly.com/question/14524058
