A solid sphere of mass 2kg and redius 1m is free to rotate about an axis passing through its center. Find a constant tangential force f required to rotate the sphere with 10 rad/sec in 2sec . Also find number of rotation made by sphere at that time interval.
Answers
Kinetic energy of rotation is
E = 1/2 I w^2,
where I is the moment of inertia and w the angular frequency of rotation.
The moment of inertia of a solid sphere of mass 2kg and radius 1m is:
Is = 2/5 *2 *1^2,
whilst that of a solid cylinder is of mass 2kg radius 1mabout its central axes is independent of its height and equals
Ic = 1/2 *2*1^2
So we want to equate the energies through
1/2 *2/5 *2*1^2 * (w_sphere)^2 = 1/2 * 1/2* 2*1^2 * (w_cyl)^2
(w_cyl)^2 = 4/5 (w_sphere)^2
w_cyl = +-sqrt(4/5) ω
(Note that the energy of rotation is independent of the direction of rotation, so we have two solutions).
Dr.
Hola!!
→ since,the force is constant , the torque produced by it and the angular acceleration à will be constant .
Hence , we can apply
W = w° + àt
⚫( Solution provided in attachment)
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