If three objects with moments of inertia I_1, I_2, and I_3 roll without slipping

Question

If three objects with moments of inertia I_1, I_2, and I_3 roll without slipping down an inclined ramp, and I_1>I_2>I_3, which object will reach the bottom of the ramp last? (Assume each object has the same mass and the same radius with respect to the axis of rotation, and that all objects begin from rest.) the object with moment of inertia I_1, the object with moment of inertia I_2. the object with moment of inertia I_3, It depends on the shape of each object. It depends on the height of the ramp. A horizontal disk rotates about a vertical axis through its center. Point 1 is halfway between the center o the disk and the edge, and Point 2 is on the edge of the disk. If the disk turns with constant angular acceleration, which statement is false? Point 1 has a linear acceleration twice as large as Point 2. Point 1 has an angular velocity twice as large as Point 2. Point 1 has the same angular acceleration as Point 2. Point 1 has a linear velocity twice as large as Point 2. Point 1 and Point 2 experience the same angular displacement in a given time span. Consider a thin disk of radius R and mass M, rolling without slipping. Which form of its kinetic energy is larger? (Remember that the moment of inertia for a thin disk is 1/2 MR^2.) Translational kinetic energy is larger than rotational kinetic energy Rotational kinetic energy Is larger than translational kinetic energy Both forms of kinetic energy have the same value. It depends on the linear speed of the ring as it rolls. A planet has two small moons in circular orbits. The first moon has a period of 12.0 hours, and an orbital distance of 6 times 10^7 meters. If the second moon has a period of 16.0 hours, what is its orbital distance? 9.24 times 10^7 meters 7.27 times 10^7 meters 4.50 times 10^7 meters 0. 3.90 times 10^7 meters While the international Space Station orbits the earth, it collects a small amount of space dust electrostatically, adding a very small amount of mass. If it could slowly add dust until the space station's mass had doubled, (meaning that the Earth's gravitational force on the space station would double) then the space station's orbital radius would also change. True False

Explanation / Answer

1) it depends on the sahpe

v = sqrt(2gh/1+c)

where c is the integer number before the formule mr^2 (like 1/2 or 2/3 or 2/5)

2) a = r*alpha

if alpha same

a1/a2 = r1/r2 = 1/2

a1 = a2/2

so 1st state ment is false

3) translationla is more that the rotational

ke t = 1/2mv^2

ker = 1/2iw^2 = 1/2mr^2w^2 = 1/4 mv^2

ket>ker

4) t is proportional to the r^3/2

so r2 = r1*(t2/t1)^2/3 = 7.27*10^7 m

5) true

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