A disc rotates with constant angular velocity ω. In the rotating frame, $F_{rot}$ = Fᵢₙ + 2m( $V_{rot}$ × $\vec{\omega}$ ) + m( $\vec{\omega}$ × $\vec{r}$ ) × $\vec{\omega}$ . A smooth radial slot is cut in a disc of radius R rotating counter-clockwise about the vertical z-axis. A small block of mass m is placed at $\vec{r}$ = (R/2)î at t = 0 and can move only along the slot.

Question

Sub-question 1

The distance r of the block at time t is:

Options

Sub-question 2

The net reaction of the disc on the block is:

Options

G1 Physics · Accepted Answer

Along the radial slot, the rotating-frame equation gives r¨=ω²r with r(0)=R/2 and ṙ(0)=0. Hence r=(R/4)( e ω t e^{ωt} e ω t + e − ω t e^{-ωt} e − ω t ). The slot reaction supplies the transverse Coriolis requirement 2mωṙ and the vertical support balances mg.