Respuesta :
Answer:
the solid sphere has the smallest moment thus angular veloicty is the largest in the system
Explanation:
One of the easiest ways to solve this exercise is by using Newton's second law for rotational motion.
τ = I α
α = τ / I
now let's use the rotational kinematics relations
w = w₀ + α t
as the bodies start from rest, their angular velocity is zero w or = 0
w = α t
we substitute
w = [tex]\frac{\tau }{I} \ t[/tex]
the body's inertia moments are
a) solid sphere I₁ = 2/5 m r²
b) spherical shell I₂ = ⅔ me r²
c) solid cylinder I₃ = ½ m r²
d) cylindrical shell I₄ = m r²
Let's analyze the expression for angular velocity, all bodies apply the same torque and it is measured in time, therefore the angular velocity is inversely proportional to the moment of inertia.
When examining the moment of inertia the largest is the moment of inertia of the cylindrical shell
the one with the lowest initial moment
we take all the values to fractions with the same denominator
I₁ = 2/5 6/6 m r² = 12/30 m r²
I₂ = ⅔ 10/10 m r² = 20/30 m r²
I₃ = ½ 15/15 m r² = 15/30 m r²
therefore the order of the moments of inertia is
I₁ <I₃ <I₂ <I₄
Therefore, since the solid sphere has the smallest moment thus angular veloicty is the largest in the system
