Formulas
The mass per unit volume of a substance.
"The density of water is approximately 1 gram per cubic centimeter."
The displacement divided by the time over which the displacement occurred.
"If a car travels 100 meters west in 5 seconds, its average velocity is 20 meters per second to the west."
The change in velocity divided by the time over which the change occurred.
"If a car increases its velocity from 0 to 60 meters per second in 5 seconds, its average acceleration is 12 meters per second squared."
The distance an object moves horizontally from its starting position.
"If a ball rolls 5 meters east on a table, its horizontal displacement is 5 meters east."
The distance an object moves vertically from its starting position.
"If a ball is thrown upward and rises to a peak of 5 meters, its vertical displacement is 5 meters upward."
A dimensionless scalar value that represents the ratio of the force of friction between two bodies and the force pressing them together.
"On a wooden table, if the coefficient of friction between the table and a book is 0.5, then the frictional force is half the force pressing the book onto the table."
The acceleration of an object moving in a circle at a constant speed, directed towards the center of the circle.
"When swinging a ball attached to a string in a circular path, the ball experiences centripetal acceleration directed toward the hand."
The force required to make an object move in a circular path, and it acts inward towards the center of rotation.
"A car turning around a curve experiences centripetal force, keeping it on the curved path."
The force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position and acts in the opposite direction.
"If a spring has a spring constant of 500 N/m, and it is displaced 0.2 meters from its rest position, the restoring force exerted by the spring is 100 N in the opposite direction of the displacement."
The energy of an object in motion, dependent on its mass and the square of its velocity.
"A car with a mass of 1000 kg traveling at a velocity of 20 meters per second has a kinetic energy of 200,000 joules."
The potential energy of an object in a gravitational field, related to its height and mass.
"If a book has a mass of 1 kg and is lifted to a shelf 2 meters high, the gravitational potential energy of the book with respect to the floor is 19.6 joules (assuming g=9.8 m/s^2)."
The rate at which work is done or energy is transferred.
"If a motor does 100 joules of work in 5 seconds, its power output is 20 watts."
The product of an object's mass and its velocity, representing the quantity of motion the object has.
"A moving car with a mass of 1000 kg and a velocity of 10 m/s has a momentum of 10,000 kg·m/s."
The rotational analog of linear momentum, dependent on an object's rotational inertia and angular velocity.
"A spinning figure skater pulls in their arms, reducing their rotational inertia, and their angular momentum causes them to spin faster."
The rotational equivalent of force, the product of the force applied and the lever arm distance from the pivot point, causing an object to rotate.
"Turning a wrench with a force of 20 N applied 0.5 meters from the bolt produces a torque of 10 N·m."
The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit, applicable for all bodies orbiting the Sun.
"If Planet X orbits the sun with a semi-major axis that is 4 times that of Earth’s, then its period will be 8 times longer than Earth’s."
The rate at which an object rotates or revolves about an axis; the change in angular displacement per unit time.
"If a wheel rotates through 2π radians in 1 second, it has an angular velocity of 2π rad/s."
The rate of change of angular velocity over time.
"When a figure skater pulls in their arms, they increase their angular acceleration and spin faster."