A small block with mass mm is placed inside an inverted cone that is rotating about a vertical axis such that the time for one revolution of the cone is TT (Figure 1). The walls of the cone make an angle ββ with the horizontal. The coefficient of static friction between the block and the cone is μsμs. If the block is to remain at a constant height hh above the apex of the cone, what are (a) the maximum value of TT and (b) the minimum value of TT? (That is, find expressions for TmaxTmax and TminTmin in terms of ββ and hh.) (c) What do your expressions for TmaxTmax and TminTmin become if μsμs = 0? Express your answer in terms of the variables ββbeta, hhh, and constants ggg, ππpi separated by a comma.
Rotational Equilibrium And Rotational Dynamics
In physics, the state of balance between the forces and the dynamics of motion is called the equilibrium state. The balance between various forces acting on a system in a rotational motion is called rotational equilibrium or rotational dynamics.
Equilibrium of Forces
The tension created on one body during push or pull is known as force.
A small block with mass mm is placed inside an inverted cone that is rotating about a vertical axis such that the time for one revolution of the cone is TT (Figure 1). The walls of the cone make an angle ββ with the horizontal. The coefficient of static friction between the block and the cone is μsμs. If the block is to remain at a constant height hh above the apex of the cone, what are (a) the maximum value of TT and (b) the minimum value of TT? (That is, find expressions for TmaxTmax and TminTmin in terms of ββ and hh.) (c)
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