- #1
StephenPrivitera
- 363
- 0
Are these quantites:
[tex]W=\int_{\theta_0}^{\theta_f}{\tau}{d}\theta=\frac{1}{2}I(\omega_f^2-\omega_0^2)[/tex]
[tex]W=\int_{r_0}^{r_f}Fdr=\frac{1}{2}m(v_f^2-v_0^2)[/tex]
the same or different?
Is "v" in the second equation the speed of the center of mass? IOW, does the bottom integral give the change in translational kinetic energy and the top the change in rotational kinetic energy (independent of each other) or do they both represent the total change in kinetic energy?
[tex]W=\int_{\theta_0}^{\theta_f}{\tau}{d}\theta=\frac{1}{2}I(\omega_f^2-\omega_0^2)[/tex]
[tex]W=\int_{r_0}^{r_f}Fdr=\frac{1}{2}m(v_f^2-v_0^2)[/tex]
the same or different?
Is "v" in the second equation the speed of the center of mass? IOW, does the bottom integral give the change in translational kinetic energy and the top the change in rotational kinetic energy (independent of each other) or do they both represent the total change in kinetic energy?