Construint in a rigid body is
a) Holonomic and rheonomic
b) Holonomic and scleronomic
c) Non- holonomic and scleronomic
d) Non- holonomic and rheonomic
Answers
Answer:
holonomic constraints are relations between the position variables (and possibly time[1]) that can be expressed in the following form:
{\displaystyle f(u_{1},u_{2},u_{3},\ldots ,u_{n},t)=0}{\displaystyle f(u_{1},u_{2},u_{3},\ldots ,u_{n},t)=0}
where {\displaystyle \{u_{1},u_{2},u_{3},\ldots ,u_{n}\}}{\displaystyle \{u_{1},u_{2},u_{3},\ldots ,u_{n}\}} are the n generalized coordinates that describe the system. For example, the motion of a particle constrained to lie on the surface of a sphere is subject to a holonomic constraint, but if the particle is able to fall off the sphere under the influence of gravity, the constraint becomes non-holonomic. For the first case the holonomic constraint may be given by the equation:
{\displaystyle r^{2}-a^{2}=0}{\displaystyle r^{2}-a^{2}=0}
where {\displaystyle r}r is the distance from the centre of a sphere of radius {\displaystyle a}a, whereas the second non-holonomic case may be given by:
{\displaystyle r^{2}-a^{2}\geq 0}{\displaystyle r^{2}-a^{2}\geq 0}
Velocity-dependent constraints such as:
{\displaystyle f(u_{1},u_{2},\ldots ,u_{n},{\dot {u}}_{1},{\dot {u}}_{2},\ldots ,{\dot {u}}_{n},t)=0}{\displaystyle f(u_{1},u_{2},\ldots ,u_{n},{\dot {u}}_{1},{\dot {u}}_{2},\ldots ,{\dot {u}}_{n},t)=0}
are not usually holonomic seIn this article learn about Constraints in physics used in classical mechanics. Constraints limit the motion of the system. We can use constraints to find the degrees of freedom that that must be calculated before solving dynamical problems.
Constraints
A constrained motion is a motion which cannot proceed arbitrarily in any manner.
Particle motion can be restricted to occur (1) along with some specified path (2) on the surface (plane or curved) arbitrarily oriented in space.
Imposing constraints on a mechanical system is done to simplify the mathematical description of the system.
Constraints expressed in the form of equation
f
(
x
1
,
y
1
,
z
1
,
…
…
,
x
n
,
y
n
,
z
n
:
t
)
=
0
are called holonomic constraints.
Constraints not expressed in this fashion are called non-holonomic constraints.
Scleronomic constraints are independent of time.
Constraints containing time explicitly are called rehonomic.
Therefore a constraint is either
Scleronomic where constraints relations does not depend on time or rheonomic where constraints relations depends explicitly on time
or
Holonomic where constraints relations can be made independent of velocity or non-holonomic where these relations are irreducible functions of velocity
Constraints types of some physical systems are given below in the table
Constraints
If a motion of the system is limited it is said to be in constrained motion. The restriction of motion is called constraints.
Rigid Body is a body where the distance between any two particles on the body is constant.
Explanation:
Rigid body motion is constrained in the sense that the distance between any two particles on the body remains constant.
The rigid body motion can be expressed as
When a constraint is expressed by equalities it is termed as holonomic constraint and those who do not are called non-holonomic constraints.
Again, if the constraint is independent of time, it is called scleronomic constraints and if it is dependent of time explicitly, then it is called rheonomic constraints.
From the above expression for rigid body motion, it is clear that it is holonomic and scleronomic.
so Constraint in a rigid body is holonomic and scleronomic.