Respuesta :
Answer:
The constant force is 263.55 newtons
Explanation:
There's a rotational version of the Newton's second law that relates the net torque on an object with its angular acceleration by the equation:
[tex]\tau = I\alpha [/tex] (1)
with τ the net torque and α the angular acceleration. It’s interesting to note the similarity of that equation with the well-known equation F=ma. I that is the moment of inertia is like m in the linear case. The magnitude of a torque is defined as
[tex] \tau = Fr\sin \theta[/tex]
with F the force applied in some point, r the distance of the point respect the axis rotation and θ the angle between the force and the radial vector that points toward the point the force is applied, in our case θ=90 and sinθ=1, then (1):
[tex]Fr = I\alpha[/tex] (2)
Because the applied force is constant the angular acceleration is constant too, and for constant angular acceleration we have that it's equal to the change of angular velocity over a period of time:
[tex] \alpha=\frac{0.800}{2.00}=0.40 \frac{rev}{s^{2}}[/tex]
It's important to work in radian units so knowing that [tex]1rev=2\pi rad [/tex]
[tex] \alpha=2.51 \frac{rad}{s^{2}}[/tex] (3)
The moment of inertia of a disk is:
[tex]I=\frac{MR^{2}}{2} [/tex] (4)
with M the mass of the disk and R its radius, then
[tex]I=\frac{(140)(1.50)^{2}}{2}=157.5 kg*m^2 [/tex]
using the values (3) and (4) on (2)
[tex]Fr = (157.5)(2.51)[/tex] (2)
Because the force is applied about the rim of the disk r=R=1.50:
[tex] F= \frac{(157.5)(2.51)}{1.50}=263.55 N[/tex]