Astudent holds one end of a thread, which is wrapped around a cylindrical spool, as shown above. the student then drops the spool from a height h above the floor, and the thread unwinds as it falls. the spool has a mass m and a radius r, and the thread has negligible mass. the spool can be approximated as a solid cylinder of moment of inertia i = 1 mr2. express your answers in terms of m, r, h, and fundamental constants. at time t = 0, the spinning spool lands on the floor without bouncing and comes free from the thread. it continues to spin, but slips on the floor's surface while doing so. assume a constant coefficient of sliding friction m. (c) calculate the angular velocity of the spool as a function of time t.

by energy conservation we know that

KE or rotation + KE of translation = gravitational PE

now we have

also we know that

now we have

now when it is rolling on ground the torque acting on it due to friction force is given by

now angular speed at any time is given as

so above is the angular speed in terms of time "t"

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards

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