E-StoreROTATION
1.MOMENT OF INERTIA
(a) CALCULATION OF MOMENT OF INERTIA BY DIGITS:
M.I about an axis of symmetry is [M] mass * the sum of squares of perpendicular semi axis
______________________________
N
where N = 3 --- for rectangular body
4 --- for elliptical (including circular)
5 --- for ellipsoidal (including spherical)
ex- for ellipse
Iz = M/4 ( a2 + b2 )
(b) The sum of moment of masses about its centre of mass is always zero.
(c) Rolling motion on an inclined plane :
velocity v = [2gs] / [
1+K2 / R2 ].
acceleration a = gsin
/ [ 1 + K2 / R2 ].
Where, s = distance of inclined plane
K = radius of gyration
R = radius of symmetrical body
(d) Angular velocity of a point whose motion is in a plane:
r2d/dt = 2v * p
where p = perpendicular from the point O upon the tangent at P to the path of the moving particle.
(e) The large moment of inertia helps keeping the motion uniform.
(f) If a number of torques acted on a system and the system is in rotational equilibrium, then clockwise torque = anticlockwise torque.
2.ROLLING MOTION ON A INCLINED PLANE
mgh = 1/2mv2 [1 + I/mr2 ]
t = 1/sin 2h [ 1 + I / mr2 ] / g
I = moment of inertia
therefore two bodies of the same shape but of different masses and radii reach the bottom at the same time.
Comments (4)
its hndwritten and also includes facts that we generally neglect in rotation............
very nice.....try 2 include some more observations tricky ones....
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