PHYS 1111Fall 09 Summaries for Chapter 9 thru 11
Rotational Motion
Angle in Radians   s (therefore the angular velocity and angular acceleration)
r
Kinematical Equations   0   t    0  0t 
Angular and Tangential s  r
v  r
1 2 2
 t   0 2  2 (   0 )
2
a  r Centripetal Acceleration ac 
1
2
  (  0 )t
v2
 r 2
r
Dynamics of Rotational Motion
Definition of Torque:  = Fl or = Flsinwhere l is the perpendicular distance to from the acting point of the
force to the pivot point and is the angle between arm and force.
Equilibrium condition for rigid bodies:  Fi  0 and  i  0
Moment of inertia: I 
 mr
2
Newton’s second law for rotational motion:  i  I
1
Rotational work (done by a torque): WR = Rotational KE = I  2
2
Total mechanical energy E 
i
1
1
mCM v 2  I  2  mgh
2
2
Angular momentum L = I (conservation if torque = 0)
Elastic and Periodic Motion
Elasticity, Stress/Strain = constant = Young’s module. Tensile stress = F/A; Tensile strain = (l-l0)/l0
Hook’s Law F = -kx; the minus sign indicates that the restoring force is against the displacement of the spring.
Period, frequency and angular frequency T = 1/f = 2/and k m 
Simple harmonic motion: x = Asin(t+); A=Amplitude and  the initial phase.
1
1
1
v   A2  x 2 then vmax = A; amax = 2A; Total mechanical energy E  mCM v 2  I  2  mgh  kx 2
2
2
2
g
mgl
Physical Pendulum  
special case: simple pendulum I = ml2,  
l
I
Damped harmonic motion, forced harmonic motion and resonance.