A small mass m is tied to a massless string and is allowed to revolve in a circl

Question

A small mass m is tied to a massless string and is allowed to revolve in a circle of radius R on a frictionless table. The other end of the string passes through a small hole in the center of the plate, and a load mass M is tied to the end of the string, see figure below. State one inertial and one non-inertial frame of reference for this problem. Calculate the speed and angular speed of the mass m such that the load mass M remains in equilibrium? State the velocity of the mass m using Cartesian coordinates. Consider that you instantaneously increase the load mass from the equilibrium established in part b). Qualitatively describe the trajectory of the small mass m.

Explanation / Answer

(a)

an inertial frame is a frame at rest or moving with a constant velocity(newton's laws are aplicable),

here M is in inertial frame.

a non inertial frame is a frame which is rotating with constant or varying angular velocity or a frame which is moving with some acceleration when seen from an inertial frame(newton's laws are aplicable),

here m is in non inertial frame.

(b)

by applying newtons laws of motion,

the weight of the M is balanced by centripugal force acting on the mass'm'.

Mg = mv^2/r

v = Mgr/m ------------(1)

we know that v = rw,

the angular velocity W = Mg/mr ----------- (2)

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