To be eligible for admission to a 3-year Bachelor of Science (B.sc) degree program in colleges affiliated with Sant Gadge Baba Amravati University, a student typically needs to have successfully completed their Higher Secondary Certificate (HSC) in either the science or Science field and maintained a consistent academic record throughout their educational career.

Title of the Course: Gravitation and Rotational Dynamics

Syllabus

Unit I – Gravitation I

• Historical perspective

• Universal Law of Gravitation

• Measurement of Gravitational Constant

• Gravitational Potential Energy, Gravitational Potential, and Gravitational Field

• Relation between Gravitational Field and Potential

• Calculation of Gravitational Potential and Field due to:

  • Point mass

  • Uniform ring

  • Uniform thin spherical shell

  • Uniform solid sphere

Unit II – Gravitation II

• Acceleration due to gravity

• Effect of altitude and depth on the value of g

• Kepler’s laws (statement only)

• Projection of satellite, critical velocity, periodic time, and binding energy

• Escape velocity of a satellite

• Weightlessness condition in a satellite

• Concept of Black Hole

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Unit III – Rotational Dynamics I

• Rigid body and torque on a rigid body

• Centre of mass and system of two particles

• Equation of motion of the centre of mass

• Rotation about a fixed axis

• Kinetic energy of a rotating body

• Moment of Inertia – physical significance and radius of gyration

• Analogy between translatory and rotatory motion

• Angular momentum and law of conservation of angular momentum

Unit IV – Rotational Dynamics II

• Theorem of perpendicular axes and theorem of parallel axes

• Calculation of moment of inertia for:

  • Annular ring

  • Circular disc

  • Solid cylinder

  • Thin rod

  • Hollow cylinder

  • Solid sphere

  • Spherical shell

• Kinetic energy of a body rolling on a horizontal plane

On successful completion of this course, students will be able to:

1. Interpret the universal law of gravitation, gravitational field, and gravitational potential.

2. Apply Kepler’s laws to describe the motion of planets and other celestial bodies.

3. Understand the motion of satellites in orbit.

4. Know the concept of a Black Hole.

5. Relate rotational motion to linear motion through angular and linear quantities.

6. Discuss the basic concepts of rotational dynamics and relate them to practical examples.

7. Apply the parallel axes theorem and perpendicular axes theorem to calculate moments of inertia.

8. Discuss real-world applications of rotational mechanics, such as the dynamics of rotating machinery and vehicles.