Kinetic energy of rotation
K =
revolution per second
angular velocity rad/sec
moment of inertia about an axis passing through centre of solid sphere
Kinetic energy of rotation
As the child stand up then Centre of mass is shifted in upwards direction from the sitting position of child, thus decreasing the effective length of the swing, so as the time period is proportion to square root of length, thus time period decreases.
time period
Time period of swing decreases as effective length decreases.
Axial vector represent rotational effect and are always along the axis of rotation. Direction of angular momentum always along the axis of rotation in accordance with right hand screw rule. Hence angular momentum is an axial vector.
if r is perpendicular to p (in case of circular motion)
L = mvr
Moment of inertia of ring or circular loop about axis passing through centre of mass and perpendicular to plane is MR2 ,
Applying perpendicular axis theorm
Here I = Moment of inertia about axis passing through diameter
As moment of inertia in terms of radius of gyration (k) is Mk2
I = Mk2
Hence direction of angular momentum is perpendicular to both and that is perpendicular to the orbital plane.
Moment of inertia of a disc about axis passing through Centre of mass and perpendicular to plane
if I = Moment of inertia of a disc about axis passing through its edge and perpendicular to plane
applying parellal axis theorm
applying perpendicular axis theorm
I = moment of inertia about a axis passing through diameter
I = 100 gm cm2
if L = const.
then
When a dancer is spinning, she has a certain angular momentum. When the dancer folds her arms, the distance of all the points of her body decreases with respect to axis of rotation so that her moment of inertia decreases. Thus, in order to conserve angular momentum, the speed of rotation has to increase and hence the dancer spins faster.
Hence if moment of inertia decrease then kinetic energy will increase.
Moment of inertia of rod about an axis through its one end and perpendicular to its length
M = 2 Kg
L = 1 m
Moment of inertia of rod in terms of radius of gyration
I = Mk2