System of particles Flashcards
(25 cards)
In pure translation motion all the particles of the object have the same ______ at any instant of time and therefore the object can be considered a _________
velocity
point object
Why cant we consider a wheel as a single particle?
different parts of the wheel in motion have different velocities and acceleration
What is a rigid body?
a body with definite and unchanging shape
In a rolling motion, what is the velocity of the point of object that is in contact with the surface ?
zero
What is rolling without slipping?
is a combination of translation and rotation where the point of contact is instantaneously at rest.
What happens when an object experiences pure rotational motion about its center of mass?
all of its points move at right angles to the radius in a plane perpendicular to the axis of rotation with a speed proportional to the distance from the axis of rotation…
In rotation of a rigid body about a fixed axis, every particle of the body moves in a ______ , which lies in a plane _______ to the axis and has its centre on the ______
circle
perpendicular
axis
examples of rotation about fixed axis
ceiling fan and potters wheel
what is precession? example
is the axis fixed?
is a change in the orientation of the rotational axis of a rotating body, i.e movement of the axis about the vertical
example : spinning top
may not be
What happens when an object experiences pure rotational motion about its center of mass?
all of its points move at right angles to the radius in a plane perpendicular to the axis of rotation with a speed proportional to the distance from the axis of rotation
motion of a rigid body which is not pivoted or fixed in some way is either ________ or a combination of ________-
pure translational
translational + rotational (rolling motion)
The motion of a rigid body which is pivoted or fixed in some way is _________ and it may be about a axis that is fixed or may not be
rotation
what is centre of mass?
a point at which the whole of the mass of the body or all the masses of a system of particle appeared to be concentrated
position of centre of mass of a n particles system in one dimension (x axis)
x = m1x1 + m2x2 / m1 + m2
position of centre of mass when masses are equal
x = x1 +x2 / 2
position of centre of mass of n particles in two dimension (x,y)
x = Σm(i)x(i) / M , y = Σm(i)y(i) / M
position of centre of mass of n particles in three dimension (x,y,z)
x = Σm(i)x(i) / M , y = Σm(i)y(i) / M , z = Σm(i)z(i) / M
position vector of COM of particles in space
r = xi + yj + zk R = Σm(i)r/ M
if the COM of system lies on the origin, then vector R is?
zero
in a body of continuous distribution of mass, the number of particles is _____ and so its impossible to carry out summations over individual particles and the spacing between the particles is _____
large
very small
in a body of continuous distribution of mass, u have to change the summations to?
integrals
position of COM and position vector in continuous distribution of mass bodies
x = ∫xdm/M , y =∫ydm/M , z=∫zdm/M
R = ∫rdm/M
position of COM of uniform laminar objects
x = Σx(i)A(i) / ΣA(i)
how many dimensions is a laminar object
2
