System of Particles and Rotational Motion 2 Flashcards
what is angular velocity
the angular velocity of a body can be defined as the rate of change of angular displacement.
It is a vector quantity and it acts along the axis of rotation of body. ( if body moves clockwise, it is upward, if anticlockwise, it is downward)
w=dtheta/dt
v = w x r
we
may characterise pure rotation by all parts of
the body having the same angular velocity at
any instant of time
what is angularacceleration
it is the rate of change of angular velocity
alpha= dw/dt
axial vector
define torque
Torque is the rotational analogue of force
tau= r x F
it is a vector quantity and an axial vextor
Nm
it is also c/a couple or moment of force
torque depends upon:
(i) Magnitude of applied force
(ii) distance of point of application of force from axis of rotation
(iii) angle between applied force and axis of rotation
what are some other ways of defining torque
(i)τ =(r sinθ ) F = r⊥ F
It is defined as the product of force and the perpendicular distance of the point of application from axis of rotation
(ii)τ =(F sinθ ) r = F⊥ r
It can be defined as the product of the radius and the tangential component of force.
how does direction of torque affect motion
when force is applied at a distance in the anticlockwise direction, then the torque acting is upward so body rotates upward. (helps in looseining)
when force is applied at a distance in the clockwie direction, the torque is acting downward and hence body moves downard
what is angular momentum
it is the rotational analogue of momentum.
l = r × p
gnitude of p and θ is the angle
between r and p. We may write
l r p = ⊥ or r p⊥
(7.26b)
where r⊥
(= r sinθ) is the perpendicular distance
of the directional line of p from the origin and
p p ⊥
( sin ) = θ is the component of p in a direction
perpendicular to r.
it is an axial vector
what is moment of inertia
it is the rotational analogue of mass. it is twice the kinetic enery of a rotating body if it rotates with unit angular veloicyt.
denotes by letter i (capital )
I= mr^2
As the mass of a body resists a change in
its state of linear motion, it is a measure of its
inertia in linear motion. Similarly, as the
moment of inertia about a given axis of rotation
resists a change in its rotational motion, it can
be regarded as a measure of rotational inertia
of the body; it is a measure of the way in which
different parts of the body are distributed at
different distances from the axis.
Unlike the
mass of a body, the moment of inertia is not a
fixed quantity but depends on the orientation
and position of the axis of rotation with respect to body and the distrubution of mass about the axis.
bodies with greater I, the greater the resistance of the body to a change in its angular velicity
what is the use of flywheel
The machines, such as steam engine and the
automobile engine, etc., that produce rotational
motion have a disc with a large moment of
inertia, called a flywheel. Because of its large
moment of inertia, the flywheel resists the
sudden increase or decrease of the speed of the
vehicle. It allows a gradual change in the speed
and prevents jerky motions, thereby ensuring
a smooth ride for the passengers on the vehicle.
conservation of angular momentum
in the absence of an external torque, the angular momentum is conserved.
when answering theory, must mention:
external torque=0
moment of inertia increase/decrease
ang velocity increase r descrease
+what is the equilibrium of a particle
condition (i)
a body is rotational equilibrium if the net external torque acting on it 0
condition (ii)
a body is translational equilibrium if the net external force acting on it is 0
condition (iii)
a body is complete mechanical equilibrium if the net force and net torque acting on the body is 0. angular and linear momentum is conserved
what is partial equilibrium
a body is said to be in partial equilibrium if it has translational but not rotational equilibrium or rotational equilibrium but not translation equilibrium
when 2 forces are acting on the same direction, the net torque is 0 so rotational eqilibrium but no translational
when 2 forces are acting in different direction, the net torque is not 0, so translational equilbirum but not rotational equilibrium.
what is a couple/
A pair of equal and opposite forces with
different lines of action is known as a couple
or torque. A couple produces rotation without
translation.
what is a principle of moments
sum of clockwise moments= sum of anticlockwise moments
anticlockwise=+ve
clockwise=-ve
what is mechanical advantage
the ratio of load to effort is mechanical advantage.
d1F1 =d2 F2
or load arm × load = effort arm × effort
The above equation expresses the principle
of moments for a lever. Incidentally the ratio
F1/F2 is called the Mechanical Advantage (M.A.);
M.A. = F1/F2
=d2/d1
If the effort arm d2 is larger than the load
arm, the mechanical advantage is greater than
one. Mechanical advantage greater than one
means that a small effort can be used to lift a
large load.
