Uniform Circular Motion

Uniform Circular Motion

• An object moving in a circle at a constant speed has uniform circular motion. • Although the object has a constant speed, its velocity constantly changes due to the change in direction. • At every point, the object's velocity is tangent to the circle. • To maintain uniform circular motion, an object requires a centripetal force (inward-directed force) and centripetal acceleration. • The centripetal acceleration can be calculated using the equation, measured in m/s^2.

Projectile Motion

• A projectile is an object launched with an initial velocity, following a parabolic path under gravity, assuming negligible air resistance. • The motion can be described using kinematic equations to determine variables such as final velocity, maximum height, and range. • The horizontal and vertical components of motion are independent and need to be analyzed separately. • The equations of motion can be used to solve projectile motion problems.

Force and Acceleration

• A force can be felt as a push or pull on an object. • Applied forces can change the state of rest or motion of an object, its direction of motion, or its shape and size. • Forces are vector quantities with both magnitude and direction. • Forces can be divided into contact forces (frictional, tension, spring force) and non-contact forces (gravity, electrostatic, magnetic).

Newton's Laws of Motion

• Newton's First Law: objects at rest remain at rest, objects in motion remain in motion, unless acted upon by an unbalanced force. • Newton's Second Law: F = ma, where F is the net force, m is the mass, and a is the acceleration. • Newton's Third Law: for every action force, there is an equal and opposite reaction force.

Acceleration

• Acceleration is the rate of change of velocity of an object. • Acceleration is associated with force, and increases with increasing force, and decreases with increasing mass. • When an object falls, air resistance decreases the rate of acceleration, and the object reaches terminal velocity.

Normal Force

• Normal force is a contact force that counteracts the weight of an object, stopping it from falling. • Normal force is not an action-reaction pair with weight, as they have different directions and magnitudes. • The magnitude of the normal force depends on the position of the surface supporting the object.

Friction

• Friction is a force that resists the relative motion of two materials against each other. • There are different types of friction, including dry friction (static and kinetic) and air resistance. • Friction depends on the materials involved, their size, surface, acceleration, and direction.

Buoyancy

• Buoyancy is the upward force exerted by a fluid on an object, equal to the weight of the fluid displaced by the object. • Archimedes' principle can be used to derive the buoyancy formula: Fb = pgV. • The buoyant force can be used to determine whether an object floats, sinks, or remains at the same depth in a fluid.

Momentum

• Linear momentum (p) of a mass moving at a velocity (v) is p = mv. • Total momentum of a system is the sum of all individual momenta. • Newton's second law is the time rate of change of the momentum. • The impulse-momentum theorem relates momentum to force and time.### Momentum

• Momentum is a quantity of motion equal to the product of the mass and velocity of an object.
• An object with more mass or velocity has more momentum.
• Conservation of momentum states that momentum is neither created nor destroyed, but only moves from one place to another.
• The equation for conservation of momentum is: (m1v1 + m2v2) before = (m1v1 + m2v2) after.

Work

• Work is a quantitative term in physics, defined as the dot product of two vectors, force and displacement.
• Work has the units of Joules (J), which is equal to Newtons-meter (Nm).
• Work is a scalar quantity, meaning it doesn't depend on the direction.
• Work can be positive, negative, or zero depending on the direction of the vectors and the angle between them.

Energy

• Energy is defined as the ability to do work or cause change.
• Energy is typically measured in units of Joules (J), but can be converted to other units.
• Energy can be classified as kinetic energy (energy in motion) or potential energy (stored energy).
• The law of conservation of energy states that energy is never created nor destroyed, but rather transformed as it moves through a system.

Work-Energy Theorem

• The work-energy theorem states that the total amount of work done on an object is equal to the change in its kinetic energy.
• Kinetic energy is energy in motion, while potential energy is the energy possessed by an object due to its position.
• An increase in energy means that positive work is done, and a decrease in energy means that negative work is done.

Law of Conservation of Energy

• The law of conservation of energy is a fundamental concept of science, stating that energy cannot be created or destroyed, only transformed from one form to another.
• The law is applied in various branches of physics and engineering, including thermodynamics.
• The First Law of Thermodynamics is an extension of the Law of Conservation of Energy.

Mechanical Energy

• Mechanical energy is the sum total of energy within a macroscopic system, including both potential and kinetic energy.
• Mechanical potential energy is stored energy, relative to an opposing force.
• Kinetic mechanical energy depends on the velocity and mass of the object that is moving.
• The law of conservation of energy states that energy can be transformed, but never created or destroyed.

Pulley Systems

• The four types of pulley systems include fixed, moveable, compound, and complex.
• Each type of pulley system serves a distinct purpose in affecting the input force needed to lift or lower an object.
• The law of conservation of energy applies in pulley systems, where energy is neither created nor destroyed.

Conservation of Mechanical Energy

• The law of conservation of mechanical energy states that, for a closed system free from dissipative forces, energy is conserved.
• The conservation of mechanical energy formula is: ΔE = 0, where ΔE is the change in mechanical energy.
• Mechanical energy can change forms, but is conserved for a conservative force, such as gravity, but not for a nonconservative force, such as friction.

Uniform Circular Motion

• An object moving in a circle at a constant speed has uniform circular motion. • Although the object has a constant speed, its velocity constantly changes due to the change in direction. • At every point, the object's velocity is tangent to the circle. • To maintain uniform circular motion, an object requires a centripetal force (inward-directed force) and centripetal acceleration. • The centripetal acceleration can be calculated using the equation, measured in m/s^2.

Projectile Motion

• A projectile is an object launched with an initial velocity, following a parabolic path under gravity, assuming negligible air resistance. • The motion can be described using kinematic equations to determine variables such as final velocity, maximum height, and range. • The horizontal and vertical components of motion are independent and need to be analyzed separately. • The equations of motion can be used to solve projectile motion problems.

Force and Acceleration

• A force can be felt as a push or pull on an object. • Applied forces can change the state of rest or motion of an object, its direction of motion, or its shape and size. • Forces are vector quantities with both magnitude and direction. • Forces can be divided into contact forces (frictional, tension, spring force) and non-contact forces (gravity, electrostatic, magnetic).

Newton's Laws of Motion

• Newton's First Law: objects at rest remain at rest, objects in motion remain in motion, unless acted upon by an unbalanced force. • Newton's Second Law: F = ma, where F is the net force, m is the mass, and a is the acceleration. • Newton's Third Law: for every action force, there is an equal and opposite reaction force.

Acceleration

• Acceleration is the rate of change of velocity of an object. • Acceleration is associated with force, and increases with increasing force, and decreases with increasing mass. • When an object falls, air resistance decreases the rate of acceleration, and the object reaches terminal velocity.

Normal Force

• Normal force is a contact force that counteracts the weight of an object, stopping it from falling. • Normal force is not an action-reaction pair with weight, as they have different directions and magnitudes. • The magnitude of the normal force depends on the position of the surface supporting the object.

Friction

• Friction is a force that resists the relative motion of two materials against each other. • There are different types of friction, including dry friction (static and kinetic) and air resistance. • Friction depends on the materials involved, their size, surface, acceleration, and direction.

Buoyancy

• Buoyancy is the upward force exerted by a fluid on an object, equal to the weight of the fluid displaced by the object. • Archimedes' principle can be used to derive the buoyancy formula: Fb = pgV. • The buoyant force can be used to determine whether an object floats, sinks, or remains at the same depth in a fluid.

Momentum

• Linear momentum (p) of a mass moving at a velocity (v) is p = mv. • Total momentum of a system is the sum of all individual momenta. • Newton's second law is the time rate of change of the momentum. • The impulse-momentum theorem relates momentum to force and time.### Momentum

• Momentum is a quantity of motion equal to the product of the mass and velocity of an object.
• An object with more mass or velocity has more momentum.
• Conservation of momentum states that momentum is neither created nor destroyed, but only moves from one place to another.
• The equation for conservation of momentum is: (m1v1 + m2v2) before = (m1v1 + m2v2) after.

Work

• Work is a quantitative term in physics, defined as the dot product of two vectors, force and displacement.
• Work has the units of Joules (J), which is equal to Newtons-meter (Nm).
• Work is a scalar quantity, meaning it doesn't depend on the direction.
• Work can be positive, negative, or zero depending on the direction of the vectors and the angle between them.

Energy

• Energy is defined as the ability to do work or cause change.
• Energy is typically measured in units of Joules (J), but can be converted to other units.
• Energy can be classified as kinetic energy (energy in motion) or potential energy (stored energy).
• The law of conservation of energy states that energy is never created nor destroyed, but rather transformed as it moves through a system.

Work-Energy Theorem

• The work-energy theorem states that the total amount of work done on an object is equal to the change in its kinetic energy.
• Kinetic energy is energy in motion, while potential energy is the energy possessed by an object due to its position.
• An increase in energy means that positive work is done, and a decrease in energy means that negative work is done.

Law of Conservation of Energy

• The law of conservation of energy is a fundamental concept of science, stating that energy cannot be created or destroyed, only transformed from one form to another.
• The law is applied in various branches of physics and engineering, including thermodynamics.
• The First Law of Thermodynamics is an extension of the Law of Conservation of Energy.

Mechanical Energy

• Mechanical energy is the sum total of energy within a macroscopic system, including both potential and kinetic energy.
• Mechanical potential energy is stored energy, relative to an opposing force.
• Kinetic mechanical energy depends on the velocity and mass of the object that is moving.
• The law of conservation of energy states that energy can be transformed, but never created or destroyed.

Pulley Systems

• The four types of pulley systems include fixed, moveable, compound, and complex.
• Each type of pulley system serves a distinct purpose in affecting the input force needed to lift or lower an object.
• The law of conservation of energy applies in pulley systems, where energy is neither created nor destroyed.

Conservation of Mechanical Energy

• The law of conservation of mechanical energy states that, for a closed system free from dissipative forces, energy is conserved.
• The conservation of mechanical energy formula is: ΔE = 0, where ΔE is the change in mechanical energy.
• Mechanical energy can change forms, but is conserved for a conservative force, such as gravity, but not for a nonconservative force, such as friction.