Answer:
Solid sphere would arrive at the bottom first.
Explanation:
According to Newton 2nd law, the angular acceleration is the ratio of torque over moment of inertia
[tex]\alpha = \frac{T}{I}[/tex]
So the one with higher acceleration would win the race.
Given that they are on the same incline and rotate without slipping. They also have the same mass and radius. So the torque must be the same. Therefore, the shape with the least moment of inertia I would win the race
since 2/3 = 0.667 > 1/2 = 0.5 > 2/5 = 0.4
Then [tex]\frac{2}{3} MR^2 > \frac{1}{2} MR^2 > \frac{2}{5} MR^2[/tex]
[tex]I_{spherical shell} > I_{cylinder} > I_{sphere}[/tex]
So the solid sphere would arrive at the bottom first.
Answer:
The solid sphere will arrive at the bottom first.
Explanation:
From the question, the 3 objects start from the same height and roll without slipping down the same incline plane. We are also told that they have the same mass and radius. So, we can say they will have same torque.
Thus,
The solid sphere (I_s) has the moment of inertia of 2MR²/5 = 0.4MR²
That of the spherical shell (Isp) is 2MR²/3 = 0.67MR²
That of the cylinder is ½•MR² =0.5 MR²
Inspecting the values of the moment of inertia, The moment of inertia for spherical shell is the largest thereby having a greater resistance to motion. While the moment of inertia of the solid sphere is the least thereby having least resistance. Thus, least resistance would lead to faster speed and thus the solid sphere will have the greater speed and will arrive first.
