Two different rigid objects, P and Q

PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

Two different rigid objects, P and Q, are tested on the same apparatus. For each object the rotational kinetic energy is measured over a range of angular speeds, and the data are plotted on a log–log graph with

\log K

on the vertical axis and

\log \omega

on the horizontal axis. The plotted points for each object fall on straight lines that are parallel to each other. For object P the point corresponding to an angular speed of

20\,\text{rad/s}

lies at a rotational kinetic energy of

2.4\,\text{J}

, while for object Q the point at the same angular speed lies at

3.6\,\text{J}

. (1) Explain what the common slope of the two lines implies about how rotational kinetic energy depends on angular speed for both objects. (2) Using the information given, determine the ratio of the moments of inertia

I_{Q}/I_{P}

. Show your reasoning. (3) Object P is known to be a uniform solid disk of mass

0.80\,\text{kg}

and radius

0.18\,\text{m}

. Using appropriate expressions, calculate its theoretical moment of inertia and evaluate whether the experimental ratio found in part (b) is consistent with this information. Provide justification for your conclusion.

Related theory

Browse the problem library