Physics $109$ General Physics I

Assignment $8$

The Conceptual Questions are worth $5$ points each, the Complete Solution Questions are worth $10$ points each. You will be graded on the physics content of your answer as well as on its structure and conciseness. For the whole assignment, remember, as with everything, neatness counts.

Conceptual Questions: These questions are to be answered with a short paragraph, except if otherwise indicated.

Problem $1.$ One of the effects of a significant global warming will be the melting of the polar ice caps. Would that change the length of the day? Explain.

Problem $2.$ Answer YES or NO: $($i$)$ Is it possible to calculate the torque that a force creates, without specifying the axis of rotation?; $($ii$)$ Is the torque created by a particular force dependent on the location of the axis of rotation?; $($iii$)$ Is the net torque acting on a body dependent on the axis of rotation?

Complete Solution Questions: These problems are to be answered with detailed calculations.

Problem $3.$ Two identical thin rectangular sheets have dimensions $0\mathrm{.}30m0\mathrm{.}50m.$ They are both set to rotation by the same torque, but the first one rotates about an axis which lies on its $0\mathrm{.}30$ m side, while the second one rotates about an axis which lies on its $0\mathrm{.}50$ m side $($Fig$.1).$ The first sheet reaches its final angular velocity in $8\mathrm{.}0$ s $,$ starting from rest. How long will it take the second sheet to reach the same angular velocity, also starting from rest.

Figure $1$: Two identical sheets rotating about a different axis.

Problem $4.$ An object of mass $m=12\mathrm{.}0kg$ is attached to a cord that is wrapped around a wheel with a radius $r=10\mathrm{.}0cm($see Fig. $2).$ The acceleration of the object down the frictionless incline is measured to be $a=2\mathrm{.}00\frac{m}{s^2}$ and the incline makes an angle $=$

$1$