Respuesta :
The Newtos's second law and kinematics for the rotational movementa llows to find the result for the order of the velocities of the bodies is:
hoop < hollow sphere < solid cylinder < solid sphere
Newton's second law for rotational motion states that the net torque is proportional to the moment of inertia and the angular acceleration of the body.
∑ τ = I α
where the bold letters indicate vectors, τ is the torque, I the moment of inertia and α the angular acceleration.
The moments of inertia of bodies with high symmetry are tabulated.
Solid cylinder I = ½ m R²
ring I = m R²
Solid sphere I = [tex]\frac{2}{5}[/tex] m R²
hollow sphere I = ⅔ m r²
look for the acceleration of each object.
A) Solid cylinder.
[tex]a_1 = 2 \frac{\sum \tau }{m R^2}[/tex]
a₁ = 2 a₀
B) hoop or Ring.
[tex]a_o = \frac{\sum \tau}{m R^2}[/tex]
C) Solid sphere.
[tex]a_2 = \frac{5}{2} \ \frac{\sum \tau}{m R^2 }[/tex]
a₂ = 2.5 a₀
D) Hollow sphere.
[tex]a_3 = \frac{3}{2} \ \frac{\sum \tau}{mR^2 }[/tex]
a₃ = 1.5 a₀
if the bodies leave with the same initial velocity, the acceleration determines which one goes faster.
w = w₀ + α t
suppose that the initial speed is zero.
w = α t
Let us calculate the velocity for the bodies after 30 s.
hoop.
w = 30 a₀
solid cylinder.
w = 60 a₀
solid sphere.
w = 75 a₀
hollow sphere.
w = 45 a₀
In conclusion using Newton's second law and kinematics for rotational movement we can find the result for the order of the velocities of the bodies are:
hoop < hollow sphere < solid cylinder < solid sphere
Learn more here: brainly.com/question/24692653
