- 1. Analytical mechanics is a branch of theoretical physics that is concerned with the description of motion and interaction of physical systems using mathematical models and analysis. It builds upon classical mechanics and is characterized by its use of calculus and mathematical formulations to derive equations of motion. By analyzing the forces and energies involved in a system, analytical mechanics aims to provide a comprehensive understanding of the dynamics and behavior of physical objects. This approach enables scientists and engineers to predict the motions of objects, study the stability of systems, and develop solutions to complex problems in various fields such as aerospace engineering, robotics, and physics research.
In classical mechanics, what is the rotational analog of force?
A) Velocity
B) Torque
C) Acceleration
D) Momentum
- 2. What is the work-energy principle?
A) The force required to keep an object moving at a constant speed
B) The definition of potential energy
C) The work done on an object is equal to its change in kinetic energy
D) The relationship between torque and angular acceleration
- 3. In a system where no external forces act on it, what is conserved?
A) Kinetic energy
B) Gravitational potential energy
C) Momentum
D) Mechanical energy
- 4. What is the equation for linear momentum?
A) p = mv
B) F = ma
C) E = mc2
D) W = Fd
- 5. In a simple pendulum, what affects the period of its swing?
A) Mass of the bob
B) Length of the pendulum
C) Angle of release
D) Initial velocity
- 6. What is the condition for an object to be in equilibrium?
A) The object must have zero momentum
B) The object must be at rest
C) The object must have constant velocity
D) The net force and net torque acting on the object are both zero
- 7. What happens to kinetic energy in an inelastic collision?
A) It increases
B) It is not conserved and is converted into other forms of energy, such as thermal energy
C) It decreases
D) It remains constant
- 8. What is the equation for angular acceleration?
A) a = Δv / Δt
B) F = ma
C) T = Fd
D) α = Δω / Δt
- 9. What is the third law of motion proposed by Newton?
A) For every action, there is an equal and opposite reaction
B) Energy is always conserved
C) Force equals mass times acceleration
D) An object at rest stays at rest
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