Chapter 5

• Kinematics of Uniform Circular Motion: motion in a circle of constant radius at constant speed.
• Instantaneous velocity in uniform circular motion is always tangent to the circle.
• The acceleration in uniform circular motion is called the centripetal, or radial, acceleration, and it points towards the center of the circle.
• There is a centripetal force, which is the mass multiplied by the centripetal acceleration.
• An object in uniform circular motion has a centripetal acceleration.
• Newton’s law of universal gravitation: Satellites are able to stay in Earth orbit because of their large tangential speed.
• An object moving in a circle at constant speed is in uniform circular motion.
• The centripetal force may be provided by friction, gravity, tension, the normal force, or others.
• For an object to be in uniform circular motion, there must be a net force acting on it.
• The force in uniform circular motion must be inward, as demonstrated by a ball on a string.
• There is no centrifugal force in uniform circular motion; what happens is that the natural tendency of the object to move in a straight line must be overcome.
• If the centripetal force vanishes, the object flies off tangent to the circle.
• When a car goes around a curve, there must be a net force towards the center of the circle of which the curve is an arc.
• If the road is flat, the force towards the center of the circle is supplied by friction.
• If the frictional force is insufficient, the car will tend to move more nearly in a straight line, as the skid marks show.
• As long as the tires do not slip, the friction in uniform circular motion is static.
• Kepler’s laws can be derived from Newton’s laws.
• Objects in orbit are said to experience weightlessness.
• The ratio of the square of a planet’s orbital period is proportional to the cube of its mean distance from the Sun.
• An imaginary line drawn from each planet to the Sun sweeps out equal areas in equal times.
• Except for gravity, the forces we experience every day are due to electromagnetic forces acting at the atomic level.
• The tangential speed must be high enough so that the satellite does not return to Earth, but not so high that it escapes Earth’s gravity altogether.
• Irregularities in planetary motion led to the discovery of Neptune, and irregularities in stellar motion have led to the discovery of many planets outside our Solar System.
• Modern physics now recognizes four fundamental forces: Gravity, Electromagnetism, Weak nuclear force (responsible for some types of radioactive decay), Strong nuclear force (binds protons and neutrons together in the nucleus).
• More properly, the experience of weightlessness is called apparent weightlessness, because the gravitational force still exists.
• Kepler’s laws describe planetary motion.
• The acceleration due to gravity varies over the Earth’s surface due to altitude, local geology, and the shape of the Earth, which is not quite spherical.
• The orbit of each planet is an ellipse, with the Sun at one focus.
• Satellites are routinely put into orbit around the Earth.
• The satellite and all its contents are in free fall, so there is no normal force, leading to the experience of weightlessness.
• If the tires do start to slip, the friction is kinetic, which is bad in two ways: The kinetic frictional force is smaller than the static.
• The magnitude of the gravitational constant G can be measured in the laboratory.
• On the surface of the Earth, the local acceleration of gravity is g, and the mass of the Earth can be calculated:
• The gravitational force on you is one-half of a Third Law pair: the Earth exerts a downward force on you, and you exert an upward force on the Earth.
• The gravitational force must be proportional to both masses.
• By observing planetary orbits, Newton also concluded that the gravitational force must decrease as the inverse of the square of the distance between the masses.
• g = 9.8 m/s^2.
• For every banked curve, there is one speed where the entire centripetal force is supplied by the horizontal component of the normal force, and no friction is required.
• Newton’s realization was that the force of gravity must come from the Earth.
• Newton further realized that this force must be what keeps the Moon in its orbit.