Chapter 6: Uniform Circular Motion and Gravitation

angular velocity (ω)

the rate of change of the angle with which an object moves on a circular path, where change in angle takes place in change in time; units are radians per second (rad/s)

arc length (Δs)

the distance traveled by an object along a circular path

banked curve

the curve in a road that is sloping in a manner that helps a vehicle negotiate the curve

center of mass

the point where the entire mass of an object can be thought to be concentrated

centrifugal force

a fictitious force that tends to throw an object off when the object is rotating in a noninertial frame of reference

centripetal acceleration

the acceleration of an object moving in a circle, directed toward the center; units are m/s²

centripetal force

any net force causing uniform circular motion

Coriolis force

the fictitious force causing the apparent deflection of moving objects when viewed in a rotating frame of reference

fictitious force

a force having no physical origin

gravitational constant, G

a proportionality factor used in the equation for Newton’s universal law of gravitation; it is a universal constant—that is, it is thought to be the same everywhere in the universe

ideal angle

the angle at which a car can turn safely on a steep curve, which is in proportion to the ideal speed

ideal banking

the sloping of a curve in a road, where the angle of the slope allows the vehicle to negotiate the curve at a certain speed without the aid of friction between the tires and the road; the net external force on the vehicle equals the horizontal centripetal force in the absence of friction

ideal speed

the maximum safe speed at which a vehicle can turn on a curve without the aid of friction between the tire and the road

microgravity

an environment in which the apparent net acceleration of a body is small compared with that produced by Earth at its surface

Newton’s universal law of gravitation

every particle in the universe attracts every other particle with a force along a line joining them; the force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them

non-inertial frame of reference

an accelerated frame of reference

pit

a tiny indentation on the spiral track moulded into the top of the polycarbonate layer of CD

radians

a unit of angle measurement

radius of curvature

radius of a circular path

rotation angle

the ratio of the arc length to the radius of curvature on a circular path; where 2 radians = 360 degrees = 1 revolution

ultracentrifuge

a centrifuge optimized for spinning a rotor at very high speeds

uniform circular motion

the motion of an object in a circular path at constant speed

Conversion of radian to degrees

Relationship of Linear velocity (v) and Angular velocity

Kepler’s 1st Law

The orbit of each planet about the Sun is an ellipse with the Sun at one focus.

Kepler’s Second Law

Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal times.

Kepler’s Third Law

The ratio of the squares of the periods of any two planets about the Sun is equal to the ratio of the cubes of their average distances from the Sun

Relationship between the period and radius of a satelitte’s orbit about a larger body M