# Inertia Question

by maverick19
Tags: inertia
 P: 1 A uniform disk(I=.5mr^2), hoop(I=mr^2), and sphere(I=.4mr^2), all with the same mass and radius, can freely rotate about an axis through the center of mass (CM) of each. A massless string sis wrapped around each item. The string is used to apply a constant and equal tangential force to each object. Enter D, H, S, or none or the same for the statements. 1) The one with the smallest moment of inertia about the axis 2) The object experiencing the largest net torque 3) The object undergoing the smallest angular acceleration 4) The object with the largest angular speed after an elapsed time of 5 seconds 5) The object for which the largest amount of string has unraveled in 5 seconds 6) The object with the smallest KE(rotational) after 5 seconds 7) The object that undergoes the most rotations in 5 seconds I want to make sure I understand concept of how inertia relates so these are my answers: 1) Sphere, object with the smallest multiplier 2) Hoop, torque=I x angular accelerations so the object with the largest multiplier in the inertia 3) Sphere, mgh=.5mv^2 + .5Iw^2. .5Iw^2=.5(.5 or 1 or .4)mv^2. So if you solve for the velocity you would divide the other side of the equation by .5, 1, or .4 and dividing by .4 would give you the greatest velocity which means the a bigger s(arc length) which would give you a bigger angular acceleration 4) Sphere, same mentality as above 5) Sphere, same mentality as above 6) I'm not sure about this ne 7) Sphere I am really not sure if I understand this stuff so please help me and if I got any wrong and explanation of why would be greatly appreciated because I want to understand why. Thanks!!!!!
Mentor
P: 12,113
 2) Hoop, torque=I x angular accelerations so the object with the largest multiplier in the inertia
Check which values are the same in the 3 setups. It is not the angular acceleration.

 3) Sphere, mgh=.5mv^2 + .5Iw^2. .5Iw^2=.5(.5 or 1 or .4)mv^2.
Which h, which v? What are you calculating there at all?

 4) Sphere, same mentality as above
While this is the right answer here, it is inconsistent with your (wrong) 3. Small angular acceleration corresponds to a smaller angular velocity after 5 seconds.

6 can be solved with a correct 3 and the formula for the total energy. Alternatively, you can use 5 to answer this.

7 follows from 4 or 5.

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