Physics 1 Formulas and Equations - Kinematics, Projectile Motion, Force, Work, Energy, Power, Moment
TLDRThis video script offers a comprehensive review of essential physics formulas for first-year physics students. It covers topics such as kinematics, projectile motion, relative velocity, vectors, Newton's laws, forces, uniform circular motion, work, energy, power, springs, momentum, impulse, rotational motion, and gravitational force. The script is designed to aid students in understanding and applying these fundamental concepts, preparing them for exams and deepening their knowledge of physics.
Takeaways
- π The formula for constant speed motion is D = VT, where D is displacement, V is velocity, and T is time.
- π For constant acceleration motion, the displacement formula is D = (V_initial + V_final)/2 * T.
- π The final velocity in constant acceleration is given by V_final = V_initial + Acceleration * T.
- π In projectile motion, the only force acting is gravity, and the kinematic formulas for constant acceleration apply.
- π The maximum height and range of a projectile can be calculated using V_initial, angle of projection, and gravitational acceleration.
- π Relative velocity is the velocity of one object with respect to another and is calculated by subtracting the velocity of the second object from the first.
- π Vector components can be calculated using trigonometric functions, with VY = V * sin(Theta) and VX = V * cos(Theta).
- π Newton's laws of motion describe the relationship between force, mass, and acceleration, with F = m*a being the fundamental second law equation.
- π Work done by a force is calculated as W = F*D, and power is the rate at which work is done, P = W/T.
- π In uniform circular motion, centripetal force and acceleration are directed towards the center, with the formula for acceleration being a = V^2/R and for centripetal force being F = m*a.
- π The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy, and for conservative forces, it's equal to the negative change in potential energy.
Q & A
What is the formula for displacement with constant speed?
-The formula for displacement with constant speed is D = V * t, where D is displacement, V is velocity, and t is time.
How is velocity different from speed?
-Velocity is displacement divided by time and it has both magnitude and direction, making it a vector quantity. Speed, on the other hand, is the magnitude of velocity and does not have a direction, making it a scalar quantity.
What is the formula for final velocity in the case of constant acceleration?
-The formula for final velocity with constant acceleration is V_final = V_initial + a * t, where V_final is the final velocity, V_initial is the initial velocity, a is the acceleration, and t is the time.
How can you calculate the displacement when dealing with constant acceleration?
-For constant acceleration, the displacement can be calculated using the formula D = V_average * t, where D is displacement, V_average is the average velocity (which is (V_initial + V_final) / 2), and t is the time.
What is the formula for projectile motion in terms of horizontal and vertical displacement?
-The formula for projectile motion is D = V_initial * t + 0.5 * a * t^2 for horizontal displacement, and y_final = y_initial + V_initial * t + 0.5 * a * t^2 for vertical displacement, where D is the horizontal displacement, y_final is the final vertical position, y_initial is the initial vertical position, V_initial is the initial velocity, a is the acceleration (due to gravity), and t is the time.
How do you calculate the maximum height reached by a projectile?
-The maximum height reached by a projectile can be calculated using the formula V_initial^2 * sin^2(Theta) / (2 * g), where V_initial is the initial velocity, Theta is the launch angle, and g is the acceleration due to gravity.
What is the relationship between linear velocity and angular velocity in rotational motion?
-In rotational motion, the relationship between linear velocity (V) and angular velocity (Omega) is given by V = Omega * R, where R is the radius of the rotation.
How is work calculated in physics?
-Work (W) is calculated as the product of the force (F) applied and the displacement (D) in the direction of the force, W = F * D. For work involving an angle, it is calculated as W = F * D * cos(theta), where theta is the angle between the force vector and the displacement vector.
What is the work-energy theorem?
-The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. Mathematically, it is expressed as W_net = ΞKE, where W_net is the net work done on the object and ΞKE is the change in kinetic energy.
How is the force required to stretch a spring related to its spring constant and displacement?
-The force (F) required to stretch or compress a spring is given by F = -K * X, where K is the spring constant and X is the displacement from its natural length. The negative sign indicates that the force exerted by the spring is in the opposite direction of the applied force.
What is the formula for elastic potential energy stored in a spring?
-The elastic potential energy (PE) stored in a spring is given by PE = 0.5 * K * X^2, where K is the spring constant and X is the displacement from the spring's natural length.
How is power related to work and time in physics?
-Power (P) is defined as the rate at which work is done or energy is transferred. It is calculated as P = W / t, where W is work done and t is the time over which the work is performed.
Outlines
π Introduction to Common Physics Formulas
This paragraph introduces the video's focus on essential physics formulas, particularly those related to motion and kinematics. It emphasizes the importance of understanding these formulas for students currently studying physics or preparing for exams. The first formula discussed is for constant speed motion, where displacement (D) is equal to velocity (V) times time (T). The distinction between speed and velocity is clarified, with speed being a scalar quantity (always positive) and velocity being a vector (which can be positive or negative). The paragraph also covers formulas applicable to motion with constant acceleration, including final velocity (V_final) and displacement with examples and explanations.
π Projectile Motion and Relative Velocity
The second paragraph delves into projectile motion, explaining how the previously discussed kinematic formulas apply to objects moving solely under the influence of gravity. It covers the conditions for projectile motion and introduces the concept of the trajectory, highlighting the highest point where vertical velocity is zero. Formulas for calculating maximum height, range, and time of flight for projectiles are provided, along with a brief introduction to relative velocity, emphasizing the main equations needed to solve problems involving it.
π’ Vectors and Newton's Laws of Motion
This paragraph introduces the concept of vectors in physics, explaining how they can represent various physical quantities like velocity, acceleration, and force. It provides formulas for calculating the components of a vector based on its angle from the horizontal axis. Newton's laws of motion are then discussed, with explanations of how they relate to an object's state of motion and the forces acting upon it. The weight force and friction, including kinetic and static friction, are also defined with their respective formulas, emphasizing their importance in understanding force dynamics.
β Uniform Circular Motion and Work-Energy Principles
The fourth paragraph focuses on uniform circular motion, defining centripetal acceleration and centripetal force, and providing formulas for calculating velocity and period. It connects these concepts to work and energy principles, discussing how work is done by a force and how it relates to the change in an object's kinetic energy. The work-energy theorem is explained, along with the concept of potential energy, particularly gravitational potential energy, and its relationship with work done by gravity.
π Springs and Elastic Potential Energy
This paragraph discusses springs, starting with the concept of spring constant and the force required to stretch or compress a spring. It introduces the formula for elastic potential energy in a spring and explains how it relates to the spring's compression or extension. The paragraph also connects the concepts of work and energy to springs, explaining how work done on a spring is converted into stored energy and how the release of this energy can do work.
π‘ Power, Momentum, and Impulse
The sixth paragraph introduces the concept of power, relating it to work and energy transfer rates. It provides the formula for power and explains its connection to force and velocity. The paragraph then moves on to discuss momentum and impulse, defining them and presenting the impulse-momentum theorem. It explains how changes in momentum relate to forces and how these concepts can be applied to calculate forces in various scenarios, such as rocket propulsion and water flow from a hose.
π Rotational Motion and Angular Quantities
This paragraph explores rotational motion, starting with the relationship between angular displacement and linear displacement. It defines angular velocity and acceleration, and provides formulas relating them to linear quantities. The paragraph also covers rotational kinematics, including formulas for final angular velocity and angular displacement, and explains how they relate to linear kinematics. Inertia and rotational inertia are introduced, with formulas for different objects and scenarios, and the paragraph concludes with a discussion on torque, relating it to force and its rotational equivalent.
π Gravitational Force and Simple Harmonic Motion
The final paragraph discusses gravitational force, explaining how it works between two masses and providing the formula for calculating it. It also covers gravitational acceleration and potential energy, offering formulas and explaining their applications. The paragraph then moves on to simple harmonic motion, discussing the frequency and period of oscillations, and providing formulas for a mass-spring system. It concludes with a brief mention of the physical pendulum and resources for further learning on these and other physics topics.
Mindmap
Keywords
π‘Displacement
π‘Velocity
π‘Acceleration
π‘Projectile Motion
π‘Relative Velocity
π‘Newton's Laws of Motion
π‘Uniform Circular Motion
π‘Work and Energy
π‘Power
π‘Momentum and Impulse
π‘Rotational Motion
Highlights
Introduction to common physics formulas for motion with constant speed.
Displacement (D) equals Velocity (V) times Time (T), highlighting the relationship between distance, speed, and time.
Explanation of the difference between speed and velocity, emphasizing that speed is a scalar quantity and velocity is a vector.
Formula for motion with constant acceleration, where final velocity (V_final) equals initial velocity (V_initial) plus acceleration (a) times time (T).
Displacement formula for constant acceleration, using average velocity, and its derivation from initial and final velocities.
Introduction to kinematics, including formulas for displacement and the concept of horizontal and vertical displacement.
Explanation of projectile motion, including the role of gravity as the sole force acting on the object and the trajectory of the projectile.
Formulas for maximum height and range of a projectile, demonstrating the application of kinematic equations in projectile problems.
Discussion on relative velocity, including the basic formula and its application in various scenarios.
Overview of Newton's laws of motion, detailing the principles that govern the behavior of objects in motion or at rest.
Explanation of forces, including weight, kinetic friction, and static friction, with their respective formulas.
Introduction to uniform circular motion, including formulas for centripetal acceleration, centripetal force, and velocity.
Work, energy, and power concepts, with formulas that describe the relationship between force, displacement, kinetic energy, and power.
Springs and elastic potential energy discussion, with formulas for force, spring constant, and elastic potential energy.
Momentum and impulse definitions, along with the impulse-momentum theorem and its applications.
Rotational motion formulas, highlighting the relationship between angular displacement, linear velocity, and angular velocity.
Torque and rotational work concepts, with formulas that connect torque to force and rotational work to angular displacement.
Gravitational force and gravitational acceleration formulas, explaining the attraction between two masses and the acceleration due to gravity.
Simple harmonic motion and pendulums discussion, including formulas for period, frequency, and elastic potential energy.
Transcripts
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