Uniform Circular Motion and Gravitation (Chp 6)

centrifugal force

fictious force (force having no physical origin- nonexisting) that tends to throw an object off when the object is rotating in a non-inertial frame of reference

radius of curvature

radius of a circular path

uniform circular motion

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

center of mass

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

inertia

the tendency of an object to resist a change in its motion

Rotation Angle and Angular Velocity

Uniform circular motion is motion in a circle at constant speed. The rotation angle Δθ is defined as the ratio of the arc length to the radius of curvature: Δθ = Δs/ r where arc length Δs is distance traveled along a circular path and r is the radius of curvature of the circular path. The quantity Δθ is measured in units of radians (rad), for which 2π rad = 360o= 1 revolution. • The conversion between radians and degrees is 1 rad = 57.3 degrees • Angular velocity ω is the rate of change of an angle, ω = Δθ/Δt where a rotation Δθ takes place in a time Δt. The units of angular velocity are radians per second (rad/s). Linear velocity v and angular velocity ω are related by v=rω or ω=v/r

radians

a unit of angle measurement

centripetal force

any net force causing uniform circular motion

angular velocity

ω = ∆θ/∆t The rate of change of the angle with which an object moves on a circular path

centripetal acceleration

• Centripetal acceleration ac is the acceleration experienced while in uniform circular motion. It always points toward the center of rotation. It is perpendicular to the linear velocity v and has the magnitude ac =v2/r or ac =rω2. • The unit of centripetal acceleration is m/s2 .

arc length

∆s=r∆θ the distance traveled by an object along a circular path

rotational angle

∆θ=∆s/r the ratio of the arc length to the radius of curvature on a circular path