An object with a definite shape that does not change.
Axis of rotation
The line of which the center of a rotating circle moves about.
The angle subtended by an arc whose length is equal to the radius. θ = l/r, 360 degrees = 2π rad.
1 rev = 360 degrees = 2π rad.
(ω). ω = θ/t
Average angular velocity
(ω). ω = Δθ/Δt
Average angular acceleration
α = lim Δω/Δt
Linear and angular velocity related
v = rω
Number of complete revolutions per second. f = ω/2π
T = 1/f
Rolling without slipping
v = rω
The distance from the axis of rotation to the line along which the force acts.
AKA lever arm.
(τ) The moment of the force about the axis. τ = rF
Newton's 2nd law for rotation
τ = I α (τ is m*N, I is kgm^2)
Rotational kinetic energy
Kinetic energy of a rotating object. 1/2 Iω^2
Work done by torque
W = τΔθ
L = Iω
A plane, flying horizontally, releases a bomb, which explodes before hitting the ground. Neglecting air resistance, the center of mass of the bomb fragments, just after the explosion moves along a ___
In a game of pool, the white cue ball hits the #5 ball and stops while the #5 ball moves away with the same velocity as the cue ball had originally. The type of collision is ___
Two equal mass balls, A and B, are dropped from the same height, and rebound off the floor. The A ball rebounds to a higher position. The A ball is subjected to the greater ___ during its collision with the floor
Momentum (Kinetic Energy)
The product of an object's mass and velocity is equal to ___
Kinetic energy is never conserved for a perfectly inelastic collision free of ___
Center of Mass
Tightrope walkers walk with a long flexible rod in order to lower their __
A small object collides with a large object and sticks. Both objects experience the same magnitude of ___
For an object on the surface of the earth, the center gravity and the center of mass are the ___
Two objects move toward each other collide, and separate. If there was no net external force acting on the objects, but some kinetic energy was lost, then the collision was not elastic and total linear momentum was ___
In a baseball game, a batter hits a ball for a home run. Compared to the magnitude of the impulse imparted to the ball, the magnitude of the impulse imparted to the bat is ___
A rubber ball and a lump of putty have equal mass. They are thrown with equal speed against a wall. the ball bounces back with nearly the same speed with which it hit. the putty sticks to the wall. The ball experiences the greater ___
Kinetic energy is conserved when it is an __ collision.
the time of impact
A baseball catcher wears a glove rather than just using bare hands to catch a pitched baseball because the force on the catcher's hand is reduced because the glove increases __
two objects collide and stick together. Kinetic energy is definitely not ___
A freight car moves along a frictionless level railroad
two objects collide and bounce off each other. Kinetic energy is conserved only if the collision is ___
They are the Same
A golf ball moving east at a speed of 4 m/s, collides with a stationary bowling ball. The golf ball bounces back to west, and the bowling ball moves very slowly to the east. Neither other experiences the greater magnitude impulse ___
Two objects collide and stick together. Linear momentum is definitely __
If an object is acted on by a non-zero net external force, its momentum will not remain ___
When a cannon fires a cannonball, the cannon will recoil backward because the momentum of the cannonball and the cannon is __
The center of gravity of an object may be thought of as the __
A 100-kg football linebacker moving at 2 m/s tackles head-on an 80-kg halfback running 3 m/s. Neglecting the effects due to digging in of cleats, the halfback will drive the linebacker __
The area under the curve on an F-t graph represents __
When two cars collide and lock together both momentum and total energy is __
Same Average Force
A small car meshes with a large truck in a head-on collision. The small car and large truck experience the __
Momentum is a __ quantity
Acceleration Due to Gravity
The graph below shows the relationship between weight and mass for a series of objects, the slope of the graph represents __
If the mass of a moving object could be doubled, the inertia would be __
4x as great
compared to the inertia of a 1-kg mass, the inertia of a 4kg mass would be __
weight and momentum
a copper coin is resting on a piece of cardboard is placed on a beaker as shown in the diagram below when the cardboard is rapidly removed, the coin drops into the beaker. The properties of the coin which best explain its fall are its __
As the mass of an object decreases, its inertia will __
A 5N ball and a 10N ball are released simultaneously from a point 50m above the surface of the Earth. Neglecting air resistance, which statement is true? at the end of 3s of free-fall. the 10 N ball will have a ______ than the 5N ball.
In the diagram below, a .4kg steel sphere and a .1kg wooden sphere are located 2.0m above the ground. Both spheres are allowed to fall from rest. Best statement when they fell 1m: Both spheres have the same sped and the steel sphere has _______ then the wooden sphere.
Uniform Circular Motion
Movement in a circle at a constant velocity, v.
A = (change in velocity)/(change in time)
Centripetal Acceleration/Radial Acceleration
Acceleration towards the center of a circle (Centripetal = "center-pointing")
Centripetal Acceleration Equation
A = v²/r
The number of revolutions per second. Defined as f.
Time required to complete one revolution. Defined as T.
Equation Relating Frequency and Period
T = 1/f
Centripetal Force equation
F = mv²/r
Law of Universal Gravitation
Every particle in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This force acts along the line joining the two particles.
Law of Universal Gravitation Equation
F = G(m1m2)/r²
Value of the constant G
G = 6.67 x 10⁻¹¹ Nm²/kg²
Velocity of an object in uniform circular motion
v = (2pir)/T
Kepler's First Law of Planetary Motion
The path of each planet about the Sun is an ellipse with the Sun at one focus
Kepler's Second Law of Planetary Motion
Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal periods of time
Kepler's Third Law of Planetary Motion
The ratio of the squares of the periods T of any two planets revolving about the sun is equal to the ratio of the cubes of their mean distances s from the sun. (T1/T2)² = (s1/s2)²
Deviations; perturbations in planetary orbits helped Newton formulate the law of universal gravitation
Laws formulated by Newton
The idea that one occurrence can cause another
Kepler's Laws of Planetary Motion
A detailed description of the motion of planets about the Sun, written by Johannes Kepler
Gravitational force equation
Force of gravity is inversely proportional to the square of the distance r from the Earth's center (Force of Gravity = 1/r²
The ability to do work.
W = F * d. Measured in joules.
1 J = 1 N * m
KE = 1/2 m * v^2
Wsubnet = ΔKE
The net work done on an object is equal to the change in the object's kinetic energy.
PE = m g h
Gravitational potential energy
PEsubgravity = m g y
Fsubs = -k * x
AKA spring equation
Elastic potential energy
Elastic PE = 1/2 k * x^2
Forces which the work does not depend on the path taken rather then the initial and final positions. Eg: gravity.
Forces that its work depends on the path. Eg: friction.
Total mechanical energy
Esub2 = Esub1
Law of conservation, Esub2 = Esub1, KE + PE = KE + PE
Principle of conservation of mechanical energy
If only conservative forces are acting, the total mechanical energy of a system neither increases nor decreases in any process. It is conserved.
Law of conservation of energy
The total energy is neither increased nor decreased in any process. Energy can be transformed from one form to another, and transferred from one object to another, but the total amount remains constant.
Forces that dissipate mechanical energy rather then the total energy.