Write two factors on which centre of mass of a body does not depend.
-Added by Shruti Srivastva Physics » System Of Particles And Rotational Motion
Shruti Srivastva
(i) Change of the coordinate system, and
(ii) Force acting on the particles.
-Answered by Shruti Srivastva On 15 July 2020:06:13:21 PM
Define the term moment of momentum?
It is equal to the product of linear momentum and the perpendicular distance of its line of action from the axis of rotation.
Define angular momentum?
Angular momentum of a particle is the moment of its linear momentum its linear momentum about the axis of rotation?
Which physical quantity is represented by the product of moment of inertia and angular velocity?
Angular momentum ( L = l ω ) .
Give the physical significance of moment of inertia.
Moment of inertia of a body is the rotational inertia of the body. It is the rotational analogue of mass in linear motion.
What are the factors on which the moment of inertia of a body depends ?
(i) Mass of the body.
(ii) Distribution of mass about the axis of rotation.
What is torque? Give its SI unit.
Refer to point 8 of Glimpses.
Where does the centre of mass of a rectangular lamina lie?
The CM of a rectangle lies at the point of intersection of the diagonals of the diagonals of the rectangle.
A circular ring and a circular disc of the same radius have the same moment of inertia about the axis passing through their centre and perpendicular to their planes. What is the ratio of their masses?
1 = Mring R2 = 1/2 Mdisc R2
∴ Mring : Mdisc = 1:2
Question 10. Asked on :15 July 2020:05:48:05 PM
State the factors on which radius of gyration of a body depends.
(i) The position and orientation of the axis of rotation.
(ii) The distribution of mass of the body about the axis of rotation.
What is the dimensional formula of radius of gyration?
The dimensional formula of radius of gyrationis [M0L1T0].
Find the radius of gyration of a uniform solid sphere about its diameter?
MK2 = 2/5 MR2
∴k = √2/5 R.
What is the moment of inertia of a hollow sphere about an axis passing through its centre?
I = 2/3 MR2 , where M is the mass and Ris the radius of the hollow sphere.
What is the moment of inertia of a solid sphere about its diameter?
I = 2/5 MR2 , where M is the mass and R is the radius of the solid sphere.
Write an expression for the moment of inertia of a rod of mass 'M' and the length 'L' about an axis perpendicular to it through one end.
I = ML2 / 3
Is moment of inertia a scalar or a vector quantity?
Moment of inertia is a scalar quantity.
Write unit of moment o physical quantity?
Unit of moment of physical quantity is kg m2.
What is the analogue of mass in rotational motion?
Moment inertia is the rotationa;l analogue of mass.
Name the rotational analogue of linear acceleration?
Angular acceleration is the rotational analogue of linear acceleration.
Two bodies move in two concentric circular paths o radii r1 and r2 in the same time. What is the ratio of their angular velocities?
Angular velocity, ω = 2π/t is same for both bodies. So the ratio is 1:1.
Is the angular velocity of rotation of hour hand of a watch greater or smaller than the angular velocity o earth's rotation about its own axis?
The hour hand completes one rotation in 12 hours while the earth completes one rotation in 24 hours. So, angular velocity o hour hand is double the angular velocity of the earth, because ω = 2π/t
What is the angular velocity of the earth spinning about its own axis?
Angular veocity of the spinnig earth
= 2π/ 86400 rad s-1
A body is moving in a circle of radius r centimetre at a constant speed of v cm s-1 . What is the angular velocity?
ω = v/r rad s-1
A boat is likely to capsize if the persons in the boat stand up. Why?
If the passengers stand, The CG of the system ( boat + passengers ) is raised and so it is likely to capsize.
A planet revolves sround the sun under the effect of gravitational force exerted by the sun. Why is the torque on the planet due to the gravitational force zero?
The gravitational force acts along the line joining the planet to the sun. Vectors r and f are always parallel.
π = rF sin 0° = 0
Which physical quantity is conserved when a planet revolves around the sun?
Angular momentum of the planet is conserved when a planet revolves around the sun.
Name the physical quantity which is equal to the time rate of change of angular momentum.
Torque is the physical quantity which is equal to the time rate of change of angular momentum.
State right hand rule to find the direction of angular momemntum.
Curl the fingers of the right hand in the direction of rotation, then the thumb points in the direction of angular momentum.
What is the angular momentum of a body of a mass m moving in a circular path of radius r with constant speed v ?
Angular momentum
= Linear momentum x moment arm.
Does the total momentum of a system of particles depend upon the velocity of the centre of mass?
Total momentum = Mvcm .
Does the magnitude and direction og angular momentum depends on the choice of the origin?
Yes, he magnitude and direction of angular momentum depends on the choice of the origin
Name the constant whose dimensions are same as that of angular momentum?
Plank's constant (h) has the same dimensions as angular momentum.
What is the ratio of the SI unit to the CGS unit of angular momentum?
SI unit of angular momentum / CGS unit of angular momentum = 107
Write the SI unit of angular momentum?
SI unit of angular momentum is kg m2 s-1
Which physical quantity corresponds to moment of linear momentum?
Physical quantity corresponds to moment of linear momentum is Angular momentum.
Which physical quantity corresponds to moment o linear momentum?
Angular momentum is the physical quantity corresponds to moment o linear momentum
A body is rotating at a steady rate, is any torque acting on the body ?
No. A torque produces angular accleration.
Under what condition, is the torque zero?
As π = rF sin Θ so torque is zero if r is zero or F is zero. It is also aero if Θ = 0° or 180°.
What is the ratio SI unit to the CGS unit of Torque?
SI unit of torque/CGS unit of torque = 107.
Write the dimensional formula of torque?
Torque = [ ML2T-2 ].
Give SI unit of Torque?
SI unit of Torque is Nm .
Name the rotational analogue of force.
The rotational analogue of force is Torque.
A rigid body is one whose constituent particles retain their relative positions even when they move under the action of an external force.
What is the vector position of then centre of mass of two particles of equal mass lies?
Its position vector is the average of the position vectors of two the two particles.
Where does the centre of mass of two particles of equal mass lie?
The centre o mass of two particle of equal masses lies midway between them.
Give an example for a body, where the centre of mass lies outside the body.
The CM of a hollow sphere lies outside the body.
Give an example for a body, where the centre of mass lie inside the body.
The CM of a solid sphere lies inside the body.
Where does the centre of mass of a two particle system lie, if one particle is more massive than the other ?
Than CM will lie on the line joining the two particles, closer to the more massive particle.
What will be the nature of motion of centre of mass of isolated system?
The centre of mass of such a system remains either at rest or moves with uniform velocity.
What is an isolated system?
An isolated system is one on which no external force acts.
Where does the centre of mass of a cone lie?
The centre o mass of a cone lies in the line joining the apex to the centre of the base at a distance equal to ¼ of the length of this line from the base.
Where does the centre of mass of uniform triangular lamina lie?
Centre of mass of a triangular lamina lies at its centroid i.e. at the point of intersection of the three medians.
On what actors, does the position of centre of mass o a rigid body depend?
(i) The geometrical shape of the body.
(ii) The distribution of mass in the body.
Define centre of mass of a system.
The centre of mass os a system may be defined as the point at which the the entire mass of the system may be supposed to be concentrated. The nature of the motion of the system will remain unaffected if all the force acting on the system were applied directly on the centre o the mass of the system.