Skip to main content

What is rigid body?

A system of large number of particles in which the distance between any two particles remains fix throughout the motion is called rigid body.



Moment of inertia


Moment of inertia I is given by,


$$ I = \Sigma m_i r_i^2$$



Torque


If a force \(\vec{F}\) acts at a point, whose position vector is \(\vec{r}\); the torque due to force


$$\vec{\tau} = \vec{r} \times \vec{F}$$



Angular displacement


Angular displacement is given by, $$ \theta = \frac{s}{r} $$



Angular velocity


Angular velocity is given by,


$$\omega = \frac{d\theta}{dt}$$



Angular acceleration


Angular accceleration is given by,


$$\alpha = \frac{d\omega}{dt}$$


SI unit of angular acceleration is rad s-2. Its dimensional formula is [M0L0T-2].

Angular momentum


Angular momentum is given by $$\vec{L} = \vec{r} \times \vec{p}$$ Where \(\vec{p}\) is linear momentum of the particle and \(\vec{r}\) is position vector of the particle.



Relation between torque and angular momentum


Relation between torque and angular momentum is given $$\tau = \frac{d\vec{L}}{dt}$$




Tangential acceleration


Tangential acceleration is given by,
$$ a_T = \vec{\alpha}\times\vec{r}$$


Where \(\vec{\alpha}\) is the angular acceleration and \(\vec{r}\) is the position vector.



Centripetal acceleration


Centripetal acceleration is given by,
$$a_c = \vec{\omega}\times\vec{v}$$


Where \(\vec{\omega}\) is the angular velocity and \(\vec{v}\) is the linear velocity.

Popular posts from this blog

How many fundamental and supplementary units in SI?

In SI, there are seven base ( fundamental ) units and two supplementary units.
Base unit

Physical quantity


Unit


Symbol




Mass


Kilogram


kg




Length


Metre


m





Time


Second


s





Temperature


Kelvin


K





Electric current


Ampere


A





Luminous intensity


Candela


cd





Quantity of matter


Mole


mol




Supplementary units


Physical quantity


Unit


Symbol




Plane angle


Radian


rad





Solid angle


Steradian


sr



Conversion factor
Conversion of length

1 centimetre = 10-2 metre
1 millimetre = 10-3metre
1 micrometre = 10-6metre
1 nanometre = 10-9 metre
1 angstrom= 10-10 metre
1 fermi = 10-15 metre
1 kilometre = 103 metre
1 austronomical unit = 1AU=1.496 × 1011 metre
1 light year = 1 ly = 9.461 ×1015metre
1 mile = 1.609 ×103 metre
1 yard = 0.9144 metre
1 inch = 0.0254 metre


Conversion of time

1 mili second= 10-3 second
1 micro second = 10-6 second
1 neno second = 10-9 second
1 hour = 60 minute = 3600 second
1 day = 24 hours =86400 second
1 year = 365 day = 3.156× 107 second
1 sec = 10-8second


Conversion of mass

1 gram = 10 -3 kg
1 quintal = 100 kg
1 tonne = 1000 kg
1 slug = 14.59…

What is the Universal law of gravitation?

Force of attraction between two masses \(m_1\) and \(m_2\) is given by, $$ F = \frac{m_1 m_2}{r^2}$$ Where, r is the distance between two masses \(m_1\) and \(m_2\). G is a constant, called the Universal gravitational constant. That is called Universal law of gravitation. Acceleration due to gravity ( variation formula ) If a body is falling freely, under the effect of gravity, then the acceleration in the body is called acceleration due to gravity. Variation in acceleration due to gravity with height Acceleration due to gravity at a height h above the surface of earth is, $$g' = g (1 - \frac{2h}{R_e})$$ Where, Re is the radius of the earth. g is the acceleratin due to gravity. Variation in acceleration due to gravity with depth Acceleration due to gravity at a depth d below the surface of earth is, $$g' = g (1 - \frac{d}{R_e})$$ Where, Re is the radius of the earth. g is the acceleratin due to gravity. Variation in acceleration due to gravity with rotatio…

Differentiation formula

Fomulae of Differentiation d⁄dx (c) = 0   Where c is constant.d⁄dx (cx) = c   Where c is constant.du⁄dt = du⁄dx ⋅ dx⁄dtd⁄dx (u+v) = du⁄dx + dv⁄dxd⁄dx (uv) = u dv⁄dx + v du⁄dxd⁄dx ( xn ) = n xn-1  Where n is real number.d⁄dx un = n un-1du⁄dx   Where u is function of x.d⁄dx sin x = cos x d⁄dx cos x = -sin x d⁄dx tan x = sec2 x d⁄dx cot x = - cosec2 x d⁄dx sec x = tan x sec x d⁄dx cosec x = - cot x cosec x d⁄dx loge x = 1⁄xd⁄dx loge u = 1⁄udu⁄dxd⁄dx ( ex ) = exd⁄dx ( eax ) = a eaxd⁄dx sin ax = a cos ax d⁄dx sin (ax+b) = a cos (ax+b) d⁄dx cos ax = - a sin ax d⁄dx cos (ax+b) = - a sin (ax+b)