Untitled Quiz

Momentum, Impulse, and Collisions

• Momentum (p) is a measure of mass in motion, symbolized by p. It's a vector quantity. SI unit: kg⋅m/s.
• Impulse (J) describes the effect of force over time, changing an object's momentum. It's a vector quantity. SI unit: kg⋅m/s.
• Impulse-momentum theorem: The change in momentum of a particle is equal to the impulse of the net force acting on it during that time interval. A large force results in a large impact that is noticeable or sudden.
• Conservation of Momentum:
  • Internal forces are the forces between particles within a system.
  • External forces act on the system from outside.
  • If the vector sum of external forces on a system is zero, the total momentum of the system is constant.
• Elastic Collisions: No mechanical energy is lost. Total kinetic energy before and after the collision is the same. If a moving object hits a non-moving object, the momentum of the moving object is transferred to the non-moving object and the first one will stop moving.
• Inelastic Collisions: Total kinetic energy after the collision is less than before. In a completely inelastic collision, the colliding bodies stick together and move as one body after the collision.

Conservation of Momentum

• An isolated system is one with no external forces.
• Momentum is conserved in isolated systems.

Elastic and Inelastic Collisions

• Elastic collisions: No energy is lost or gained during the collision. The total kinetic energy remains the same.
• Inelastic collisions: Some kinetic energy is lost during the collision. The total kinetic energy after the collision is less than before. A completely inelastic collision is a type of inelastic collision where the colliding objects stick together after the collision

Center of Mass of a System

• The center of mass is the point where the system's mass is concentrated.
• The center of mass moves as if all the mass were concentrated at that point.

Coefficient of Restitution (e)

• A ratio of final relative velocity to initial relative velocity after collision.

Elastic Impact (e=1)

• The initial kinetic energy is equal to the final kinetic energy after the impact.

Completely Inelastic Impact (e=0)

• The relative velocity after the collision is zero. The colliding particles stick together and move with the same velocity.

Rotation of Rigid Bodies and Dynamics of Rotational Motion

• θ describes the rotational or angular position of a body. Counterclockwise is positive; clockwise is negative.
• 1 radian (1 rad) is the angle subtended at the center of a circle by an arc with a length equal to the radius of the circle.
• Angular velocity (ω) is the rate of rotation. SI unit: rad/s or rev/min.
• Angular acceleration (α) is the rate of change of angular velocity.

Relating Linear and Angular Kinematics

• Relationship between angle θ (in radians) and arc length s: s = rθ.
• Relationship between linear (v) and angular (ω) speeds: v = rω.

Energy in Rotational Motion

• Moment of inertia (I) is a measure of how mass is distributed with respect to an axis of rotation. It's the sum of the product of the mass of every particle with its square of the distance from the axis of rotation. SI unit: kg⋅m².
• Rotational kinetic energy: K = 1/2 Iω².

Torque

• Torque (τ) is the tendency of a force to cause rotational motion. SI unit: N⋅m.
• Torque is a vector quantity.
• Torque formula: τ = F⋅l (where F is the force and l is the lever arm).
• The direction of the torque vector is given by the right-hand rule.

Angular Momentum

• Angular momentum (L) is a measure of rotational inertia. SI unit: kg⋅m²/s.
• Angular momentum's relationship to linear momentum is the same as the relationship of torque to force.

Newton's Law of Universal Gravitation and Kepler's Laws of Planetary Motion

• Gravity acts universally among all objects in the universe. Gravitational forces always act along the line joining the two particles.
• Newton's Law of Universal Gravitation: Every particle attracts every other particle with a force that is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.
• Weight is the total gravitational force exerted on a body by all other bodies in the universe.

Gravitational Potential Energy

• Gravitational potential energy (U) is the energy an object has due to its position in a gravitational field. Formula: U = -GMm/r.

Kepler's Laws and the Motion of Planets

• Kepler's First Law (Law of Ellipses): Planets move in elliptical orbits with the sun at one focus.
• Kepler's Second Law (Law of Equal Areas): A line joining a planet and the sun sweeps out equal areas in equal intervals of time.
• Kepler's Third Law (Law of Harmonies): The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

The Motion of Satellites

• Satellites follow trajectories (paths) in space.
• Trajectories can be closed (ellipses or circles) or open (parabolas or hyperbolas).