PHYS 161H Lecture Notes - Lecture 7: Acceleration, Rotation Around A Fixed Axis, Angular Acceleration

• School: University of Arizona
• Department: Physics
• Course: PHYS 161H
• Professor: Manne

Document Summary

Non point particles, real world objects: capable of rotation. Rotation of a body about any fixed axis, place coordinate axis with origin at the fixed axis of rotation, considering the motion of a generalized point. Radius, r, angle the radial line makes with the horizontal or vertical axis, theta position given in terms of theta, Angular displacement: delta(theta)= theta(final) theta(initial) : radians (dimensionless quantity) Average angular speed or velocity: omega (w) (bar) = delta(theta)/delta(time) = s^-1 or radians per second. Instantaneous angular speed or velocity: d(theta)/d(time) = s^-1. Angular acceleration: , alpha= dw/dt= d^2(theta)/d(time)^2 = s^-2, or radians per second squared rpm=revolutions per minute, should convert to radians per second theta(t)= wdt w(t)= dt. S=r* (theta) v=r*w at=r* constant acceleration w= w0+ t theta(final)=theta(initial)+w0*t+(1/2) *t^2 w^2=(w0)^2+2 (theta(final)-theta(initial)) Initially rotating at 33rpm, turned off and comes to rest in 20 seconds (assume =constant), find . 33rpm*(2pi/1 rev)*(1min/60 sec) = 3. 46 radians per second (s^-1) wi=3. 46 s^-1 and wf=0.