Download Definitions Angular displacement θ indicates the angle through

Definitions Angular displacement θ indicates the a ngle through which a n object has rotated. It is measured in radians. Average a ngular velocity ω
is a ngular displacement divided by the time interval over which that a ngular displacement occurred. It is measured in rad/s. Instantaneous a ngular velocity is how fast a n object is rotating a t a specific moment in time. Angular Acceleration α tells how much a n object’s a ngular speed c hanges in one second. It is measured in rad/s per second. Angular a cceleration a nd c entripetal a cceleration a re independent. Angular a cceleration c hanges a n object’s rotational speed, while c entripetal a cceleration c hanges a n object’s direction of motion. Relationship between angular and linear motion The linear displacement of a rotating object is given by r θ , where r is the distance from the rotational axis. The linear speed of a rotating object is given by v = r ω The linear a cceleration of a rotating object is given by a = r α . Torque The torque provided by a force is given by τ = Fd ⊥ , where d ⊥ refers to the “ lever a rm.” (see pp. 126­127 of the 5­steps book for a more detailed summary of lever a rm.) It is a lso denoted a s τ = Fd sin θ. Rotational Inertia Rotational inertia I represents a n object’s resistance to a ngular a cceleration. For a point particle, rotational inertia is MR 2 , where M is the particle’s mass, a nd R
is the distance from the a xis of rotation. For a series of point particles, the rotational inertia is c alculated by finding the sum of the individual moments of inertia ­ I = Σ mR 2 . For a c ontinuous object we use the integral formula I = ∫ R2 dm For a c omplicated object, its rotational inertia may be given by a n e quation relating its mass a nd radius. The c hart on the next page from Giordano’s text should not be memorized, but used a s a guide. These equations will be given a s needed. Rotational inertia of multiple objects a dd together a lgebraically. Newton’s Second Law for Rotation An a ngular a cceleration is c aused by a net torque: α =