A disc is rotating with constant angular velo | vedclass

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(C) In the rotating frame of the disc,the insect experiences two pseudo-forces: the centrifugal force $F_c = m\omega^2r$ directed radially outwards an

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Greater than $r\omega^2$ in magnitude

Vedclass · Answer

(C) In the rotating frame of the disc,the insect experiences two pseudo-forces: the centrifugal force $F_c = m\omega^2r$ directed radially outwards and the Coriolis force $F_{cor} = 2m(\vec{v} 	imes \vec{\omega})$ directed perpendicular to the radial velocity. In the ground frame,the acceleration of the insect is the vector sum of radial and tangential components. The radial acceleration is $a_r = -r\omega^2$ (centripetal acceleration). The tangential acceleration is $a_t = 2v\omega$ (due to the change in tangential velocity as the insect moves radially). The total acceleration magnitude is $a = \sqrt{a_r^2 + a_t^2} = \sqrt{(r\omega^2)^2 + (2v\omega)^2}$. Since $(2v\omega)^2 > 0$,the magnitude $a = \sqrt{r^2\omega^4 + 4v^2\omega^2}$ is clearly greater than $r\omega^2$.

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