Advertisements
Advertisements
Question
Define radius of gyration. Write its physical significance.
Solution
Radius of gyration or gyradius refers to the distribution of the component of object around the axis in terms of the mass moment of inertia, As it is the perpendicular distance from the axis of rotation to a point mass m that gives an equivalent inertia to the original object m The nature of the object does not affect the concept, which applies equally to a surface bulk mass. Mathematically the radius of gyration is the root mean square distance of the object's parts from either its center of mass or the given axis, depending on the relevant application.
`"I" = "MK"^2`
`"K"^2= "I"//"M"`
`"K"= sqrt("I"//"M")`
Physical Signification:
It signifies distribution of mass about axis of rotation.
APPEARS IN
RELATED QUESTIONS
Obtain an expression for total kinetic energy of a rolling body in the form
`1/2 (MV^2)[1+K^2/R^2]`
The kinetic energy of a rotating body depends upon................
- distribution of mass only.
- angular speed only.
- distribution of mass and angular speed.
- angular acceleration only.
The body is rotating with uniform angular velocity (w) having rotational kinetic energy (E). Its angular momentum (L) is: ...............
a) `(2E)/ω`
b) `E^2/ω`
c) `E/ω^2`
d) `E/(2ω)`
The kinetic energy of emitted photoelectorns is independent of ............
(a) frequency of incident radiation.
(b) intensity of incident radiation.
(c) wavelength of incident radiation
(d) collector plate potential
If ‘L’ is the angular momentum and ‘I’ is the moment of inertia of a rotating body, then `L^2/(2I)`represents its _____
(A) rotational P.E.
(B) total energy
(C) rotational K.E.
(D) translational K.E
The radius of gyration of a body about an axis, at a distance of 0.4 m from its centre of mass is 0.5 m. Find its radius of gyration about a parallel axis passing through its centre of mass.
