EK 1001 Physics Problem # 138

[Inkoate]

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This question is on rotational inertia, so it may be beyond the MCAT material we have to study, but the underlying concepts I'm asking about are things all of us should know.

The explanation says that since the mass of the hollow ball A is concentrated on the outside, the rotational inertia of A is greater than ball B. Because of this, it accelerates at a lesser rate than B. EK further explained that static friction affects acceleration. They said that the following equation would describe its motion down the incline (mgsin(theta)- greek letter mu(mgcos(theta)). I thought that this equation applied when things are sliding, not rolling. Wouldn't these two values be added rather than subtracted.

Also, I do not agree that the static friction of B would be less than the static friction for A. Wouldn't the static friction of B be greater than A since the ball has greater acceleration than A? The net force is down the incline plane, and I'm assuming that static friction plus gravity are the forces acting in the direction of the motion.

 

[Geneticist]

Try the MCAT Q&A section for better responses. 😉

 

[ksmi117]

Moving to the MCAT Study forum.

 

[ilovemcat]

This question is on rotational inertia, so it may be beyond the MCAT material we have to study, but the underlying concepts I'm asking about are things all of us should know.

The explanation says that since the mass of the hollow ball A is concentrated on the outside, the rotational inertia of A is greater than ball B. Because of this, it accelerates at a lesser rate than B. EK further explained that static friction affects acceleration. They said that the following equation would describe its motion down the incline (mgsin(theta)- greek letter mu(mgcos(theta)). I thought that this equation applied when things are sliding, not rolling. Wouldn't these two values be added rather than subtracted.

Also, I do not agree that the static friction of B would be less than the static friction for A. Wouldn't the static friction of B be greater than A since the ball has greater acceleration than A? The net force is down the incline plane, and I'm assuming that static friction plus gravity are the forces acting in the direction of the motion.

The way I like to think of rotational inertia is, "How difficult something is to rotate." The further the mass from the axis of rotation, the more rotational inertia an object has - and therefore, the more difficult something is to rotate.

So for the two balls described above - because for ball A, the mass is located at a greater distance from the axis of rotation compared to the solid ball B (where mass acts AT the axis of rotation), ball A will have a GREATER rotational inertia. Because it has greater rotational inertia, it's more difficult to rotate.

Both balls have an equal amount of static friction. However, because ball A has a greater rotational inertia, it'll rotate slower and therefore take longer to reach the bottom.

Just like the equation for F=ma which says that for a given force, an object with a LARGER mass will accelerate slower (their inversely proportional), the same idea is true for rotational motion.

 

[Inkoate]

thanks for your reply! I think I got it.