Uniform Circular Motion

Uniform Circular Motion

• Uniform circular motion occurs when an object moves in a circle at a constant speed.
• The velocity of the object constantly changes due to its changing direction.
• The velocity of the object is always tangent to the circle at every point.
• A centripetal force (inward-directed force) and centripetal acceleration (inward-directed acceleration) are required to maintain uniform circular motion.
• The centripetal acceleration can be calculated using the equation, and the centripetal force can be calculated using the equation.

Projectile Motion

• Projectile motion is the path of an object that is launched with an initial velocity and follows a trajectory under the influence of gravity.
• Projectiles follow a predictable parabolic path determined by the initial velocity, launch angle, and acceleration due to gravity.
• Kinematic equations can be used to determine variables such as final velocity, maximum height, and range.
• The motion of projectiles in the horizontal and vertical directions is independent and must be analyzed separately.

Solving Projectile Motion Problems

• To solve projectile motion problems, equations are used to figure out the horizontal and vertical velocity components.
• The problem is approached by writing down all the given information, then using the equations to find the answer.
• It becomes an algebra problem, where the goal is to solve for the unknown variable.

Graphs of Motion

• Two graphs can be used to describe the motion of an object: position-time graph and velocity-time graph.
• The slope of a position-time graph represents the velocity of an object.
• Analyzing the motion of an object can help prove that it is moving at a constant velocity.

Projectile Motion Equations

• Equations can be used to describe projectile motion in the y-direction (vf = vi + a * t, etc.) and x-direction (vx = x / t).
• The y-direction equations involve acceleration, while the x-direction equation involves constant velocity.

Newton's Laws of Motion

• Newton's first law of motion states that an object at rest or in motion will remain at rest or in motion unless acted upon by an unbalanced force.
• The law of inertia is the resistance of an object to a change in motion.
• Balanced forces are equal in magnitude and opposite direction, while unbalanced forces cause a change in velocity.
• Newton's second law of motion states that the net force of an object is dependent on both the mass and acceleration of an object.
• Newton's third law of motion states that for every action, there is an equal and opposite reaction.

Force

• A force is a push or pull on an object with mass that causes a change in the object's motion.
• Force is measured in Newtons (N).
• Velocity is speed in a given direction.
• Applied forces can change the state of rest or motion of an object, the direction of motion, or the shape and size of the object.
• Forces can be divided into contact and non-contact forces.

Force and Vector Quantities

• Force is a vector quantity, which means it has both magnitude and direction.
• Forces are represented by free-body diagrams, which show the magnitude and direction of the force.
• Balanced forces are forces that are equal in magnitude but opposite in direction.
• Unbalanced forces cause a change in the object's state of motion.
• Net force is the vector sum of all forces acting on an object.

Newton's Second Law

• The ratio of the net force acting on an object to the object's acceleration is constant and equal to the object's mass.
• Momentum is the product of the object's mass and velocity.
• The net force is reduced by the negative effects of friction force, which slows down the average speed and creates lower acceleration.
• As the mass increases, friction increases, which reduces the net force.

Forces and Friction

• Forces can act by touching or at a distance.
• Friction is a force that opposes motion between two surfaces that are in contact.
• The two main factors that determine the force required to pull an object are the masses of the objects and the friction between them and the surface.

Galileo and Acceleration

• Galileo discovered acceleration, which is the rate of change of velocity.
• Acceleration is a change in speed, direction, or both.
• We calculate acceleration by the change in velocity over the change in time (a = ΔV/Δt).
• When air resistance is not a factor, all falling objects accelerate at the same rate: 9.8 m/s2.

Uniform Circular Motion

• Uniform circular motion occurs when an object moves in a circle at a constant speed.
• The velocity of the object constantly changes due to its changing direction.
• The velocity of the object is always tangent to the circle at every point.
• A centripetal force (inward-directed force) and centripetal acceleration (inward-directed acceleration) are required to maintain uniform circular motion.
• The centripetal acceleration can be calculated using the equation, and the centripetal force can be calculated using the equation.

Projectile Motion

• Projectile motion is the path of an object that is launched with an initial velocity and follows a trajectory under the influence of gravity.
• Projectiles follow a predictable parabolic path determined by the initial velocity, launch angle, and acceleration due to gravity.
• Kinematic equations can be used to determine variables such as final velocity, maximum height, and range.
• The motion of projectiles in the horizontal and vertical directions is independent and must be analyzed separately.

Solving Projectile Motion Problems

• To solve projectile motion problems, equations are used to figure out the horizontal and vertical velocity components.
• The problem is approached by writing down all the given information, then using the equations to find the answer.
• It becomes an algebra problem, where the goal is to solve for the unknown variable.

Graphs of Motion

• Two graphs can be used to describe the motion of an object: position-time graph and velocity-time graph.
• The slope of a position-time graph represents the velocity of an object.
• Analyzing the motion of an object can help prove that it is moving at a constant velocity.

Projectile Motion Equations

• Equations can be used to describe projectile motion in the y-direction (vf = vi + a * t, etc.) and x-direction (vx = x / t).
• The y-direction equations involve acceleration, while the x-direction equation involves constant velocity.

Newton's Laws of Motion

• Newton's first law of motion states that an object at rest or in motion will remain at rest or in motion unless acted upon by an unbalanced force.
• The law of inertia is the resistance of an object to a change in motion.
• Balanced forces are equal in magnitude and opposite direction, while unbalanced forces cause a change in velocity.
• Newton's second law of motion states that the net force of an object is dependent on both the mass and acceleration of an object.
• Newton's third law of motion states that for every action, there is an equal and opposite reaction.

Force

• A force is a push or pull on an object with mass that causes a change in the object's motion.
• Force is measured in Newtons (N).
• Velocity is speed in a given direction.
• Applied forces can change the state of rest or motion of an object, the direction of motion, or the shape and size of the object.
• Forces can be divided into contact and non-contact forces.

Force and Vector Quantities

• Force is a vector quantity, which means it has both magnitude and direction.
• Forces are represented by free-body diagrams, which show the magnitude and direction of the force.
• Balanced forces are forces that are equal in magnitude but opposite in direction.
• Unbalanced forces cause a change in the object's state of motion.
• Net force is the vector sum of all forces acting on an object.

Newton's Second Law

• The ratio of the net force acting on an object to the object's acceleration is constant and equal to the object's mass.
• Momentum is the product of the object's mass and velocity.
• The net force is reduced by the negative effects of friction force, which slows down the average speed and creates lower acceleration.
• As the mass increases, friction increases, which reduces the net force.

Forces and Friction

• Forces can act by touching or at a distance.
• Friction is a force that opposes motion between two surfaces that are in contact.
• The two main factors that determine the force required to pull an object are the masses of the objects and the friction between them and the surface.

Galileo and Acceleration

• Galileo discovered acceleration, which is the rate of change of velocity.
• Acceleration is a change in speed, direction, or both.
• We calculate acceleration by the change in velocity over the change in time (a = ΔV/Δt).
• When air resistance is not a factor, all falling objects accelerate at the same rate: 9.8 m/s2.