University:
Montgomery College
Course:
PHYS 161: General Physics I: Mechanics and Heat
Academic year:

2019
Views:

322

Pages:

2
Author:

cravelingstnw

Linear and Angular Quantities To understand the relationships between linear and angular quantities, we need to know about radians: A radian is the angle that subtends an arc length equal to the radius of the circle. r A general arc has length s = r  where r is the radius and  is the angle measured in radians Since a circle has circumference C = 2 r , this means that 2 radians = 360.  r  = 1 radian Relationship* Linear Quantity Angular Quantity Displacement s Angular Displacement   Speed v Angular Speed   Acceleration a Angular acceleration  Mass m Moment of inertia I a  The correspondence between linear and angular quantities gives us corresponding angular kinematic equations: = + = ∆ + ∆ *These relationships only hold if  is measured in radians Just as the mass of an object, m, determines its acceleration under a given force, F , its moment of inertia, I, determines its angular acceleration under a given torque, . The magnitude of the torque, , is defined as where R is the displacement from the pivot point and  is the angle between R and F . F Moment of inertia I is defined about a pivot point. For a single object (as shown)  Pivot Point P R Object with mass m I mR m1 R1 m2 R2 m3 R3 P For a collection of N objects (in the figure N = 4) R4 m4 Linear Quantity Angular Quantity Relationship Mass m Moment of inertia I (see above) Force F = m a Torque  = I   = F r sin * Translational Kinetic Energy Rotational Kinetic Energy K.E. = K.E. = Linear Momentum P = Angular Momentum L =  If there is no external torque on a system, then the total angular momentum is conserved (just as total linear momentum is conserved if there is no external force). *Here  is the angle between F and r .