A Circular Disc Of Mass ‘M’ And Radius ‘r’ Is Set Rolling On A Table. If ‘ω’ Be The Angular Velocity, Calculate Its Total Energy ‘E’.

Ans. When a circular disc of mass M and radius r rolls on a table, then its total kinetic energy E will be, = (Energy due to linear motion) +…

Continue ReadingA Circular Disc Of Mass ‘M’ And Radius ‘r’ Is Set Rolling On A Table. If ‘ω’ Be The Angular Velocity, Calculate Its Total Energy ‘E’.

Two Parallel Circular Wheels, Each Of Mass ‘M’ And Radius ‘R’ And Filled With Weightless Spokes Are Rigidly Joined Together By A Weightless Rod Of Length 2R Passing Through The Centre Of The Wheels Perpendicular To Their Planes. Calculate The Moment Of Inertia Of The Wheels About An Axis Passing Perpendicular Through The Centre Of The Rod.

Ans. Fig. 1 Here, two wheels each of mass M and radius R are rigidly connected by a weightless rod of length 2R. The moment of inertia of each wheel…

Continue ReadingTwo Parallel Circular Wheels, Each Of Mass ‘M’ And Radius ‘R’ And Filled With Weightless Spokes Are Rigidly Joined Together By A Weightless Rod Of Length 2R Passing Through The Centre Of The Wheels Perpendicular To Their Planes. Calculate The Moment Of Inertia Of The Wheels About An Axis Passing Perpendicular Through The Centre Of The Rod.

Two Particles Of Masses ‘m’ And ‘M’ Are At A Distance ‘d’ Apart. Calculate The Moment Of Inertia Of The System About An Axis Passing Through The Centre Of Mass And Perpendicular To The Line Joining The Two Masses. If ‘ν’ Be The Frequency Of Revolution, Then Also Calculate The Rotational Kinetic Energy Of The System.

Ans. Fig. 1 Here the two masses 'm' and 'M' are at a distance d apart. Let us consider, O be the centre of mass of the system of these…

Continue ReadingTwo Particles Of Masses ‘m’ And ‘M’ Are At A Distance ‘d’ Apart. Calculate The Moment Of Inertia Of The System About An Axis Passing Through The Centre Of Mass And Perpendicular To The Line Joining The Two Masses. If ‘ν’ Be The Frequency Of Revolution, Then Also Calculate The Rotational Kinetic Energy Of The System.

A Uniform Rod 2 ft Long, Weighting 5 lbs, Is Revolving 60 Times A Minute About One End. Calculate Its Moment Of Inertia And Kinetic Energy.

Ans. Here the mass of the uniform rod M=5 lbs,length of the rod is l=2 ft.The rod is rotating about one end with frequency =1 rev./sec.The angular velocity is We…

Continue ReadingA Uniform Rod 2 ft Long, Weighting 5 lbs, Is Revolving 60 Times A Minute About One End. Calculate Its Moment Of Inertia And Kinetic Energy.

Calculate The Kinetic Energy Of A Thin Rod Of Length ‘l’ And Mass ‘m’ Per Unit Length Rotating About An Axis Through The Middle Point And Perpendicular To Its Length With Angular Velocity ω.

Ans: The length of the thin rod is l and mass density i.e., mass per unit length is m. So the total mass of the rod is .The rod is…

Continue ReadingCalculate The Kinetic Energy Of A Thin Rod Of Length ‘l’ And Mass ‘m’ Per Unit Length Rotating About An Axis Through The Middle Point And Perpendicular To Its Length With Angular Velocity ω.

Two Circular Metal Discs Have The Same Mass ‘M’ And The Same Thickness ‘t’. Disc ‘1’ Has A Uniform Density, Which Is Less Than That Of The Disc ‘2’. Which Disc Has The Larger Moment Of Inertia.

Ans. For disc 1, mass and thickness are M and t respectively. Let, be the radius of the circular disc and be the uniform density of the disc. The volume…

Continue ReadingTwo Circular Metal Discs Have The Same Mass ‘M’ And The Same Thickness ‘t’. Disc ‘1’ Has A Uniform Density, Which Is Less Than That Of The Disc ‘2’. Which Disc Has The Larger Moment Of Inertia.

Obtain An Expression For The Moment Of Inertia Of A Solid Cone (i) About Its Axis Of Symmetry, (ii) About An Axis Passing Through The Vertex And Perpendicular To The Axis Of Symmetry

(i) Moment of inertia of a solid cone about its axis of symmetry: Fig. 1 Let us consider a right circular solid cone ABC of mass M and height h,…

Continue ReadingObtain An Expression For The Moment Of Inertia Of A Solid Cone (i) About Its Axis Of Symmetry, (ii) About An Axis Passing Through The Vertex And Perpendicular To The Axis Of Symmetry

Determine The Moment Of Inertia Of A Triangular Lamina (i) About One Of Its Sides, (ii) About An Axis Passing Through The Centre Of Gravity And Parallel To One Side, (iii) About An Axis Passing Through One Of Its Vertices And Parallel To Opposite Side.

(i) Moment of inertia of a triangular lamina about one of its side: Fig. 1 Let us consider a triangular lamina ABC of mass M, is rotating about one of…

Continue ReadingDetermine The Moment Of Inertia Of A Triangular Lamina (i) About One Of Its Sides, (ii) About An Axis Passing Through The Centre Of Gravity And Parallel To One Side, (iii) About An Axis Passing Through One Of Its Vertices And Parallel To Opposite Side.

Determine The Moment Of Inertia Of A Uniform Elliptic Lamina Or Elliptic Disc (i) About Its Minor Axis, (ii) About Its Major Axis, (iii) About An Axis Passing Through The Centre Of The Disc And Perpendicular To Its Plane.

(i) Moment of inertia of a uniform elliptic lamina or elliptic disc about its minor axis: Fig. 1 Let us consider a uniform elliptic lamina or elliptic disc of mass…

Continue ReadingDetermine The Moment Of Inertia Of A Uniform Elliptic Lamina Or Elliptic Disc (i) About Its Minor Axis, (ii) About Its Major Axis, (iii) About An Axis Passing Through The Centre Of The Disc And Perpendicular To Its Plane.

Calculate The Moment Of Inertia Of A Circular Ring (i) About An Axis Passing Through Its Centre And Perpendicular To The Plane Of The Ring, (ii) About An Axis Passing Through Its Centre And Lying In The Plane.

(i) Moment of inertia of a circular ring about an axis passing through its centre and perpendicular to the plane of the ring: Fig. 1 Let us consider a circular…

Continue ReadingCalculate The Moment Of Inertia Of A Circular Ring (i) About An Axis Passing Through Its Centre And Perpendicular To The Plane Of The Ring, (ii) About An Axis Passing Through Its Centre And Lying In The Plane.