- #1
flasherffff
- 10
- 0
hi ,this is my first post (and its not HW)
i currently study dynamics of rigid bodies
using (Hibbeler)
and there's one thing about this type of motion (rolling) that just seems to elude me
for any planar motion we have 3 equations
[tex]\Sigma F_{{x}}={\it ma}_{{g_{{x}}}}[/tex]
[tex]\Sigma F_{{y}}={\it ma}_{{g_{{y}}}}[/tex]
[tex]\Sigma M_{{g}}=i_{{g}}\alpha[/tex]
if i have a wheel rolling on a surface with constant velocity ,say a car wheel not connected to the engine
by kinematics [tex]a_{{g}}=\alpha\,r[/tex] then [tex]\alpha=0[/tex]
then there is a force P acting on the mass center G
then by the first equation if ag=0
then the friction force f must be equel and opposite of p and acting at the contact point A
but then by eq3 the moment about G causes an increase in [tex]\alpha[/tex]
contradicting the kinematics equation
http://img5.imageshack.us/img5/4869/scanpic0001m.jpg
now ,obviously i got something wrong but what
i currently study dynamics of rigid bodies
using (Hibbeler)
and there's one thing about this type of motion (rolling) that just seems to elude me
for any planar motion we have 3 equations
[tex]\Sigma F_{{x}}={\it ma}_{{g_{{x}}}}[/tex]
[tex]\Sigma F_{{y}}={\it ma}_{{g_{{y}}}}[/tex]
[tex]\Sigma M_{{g}}=i_{{g}}\alpha[/tex]
if i have a wheel rolling on a surface with constant velocity ,say a car wheel not connected to the engine
by kinematics [tex]a_{{g}}=\alpha\,r[/tex] then [tex]\alpha=0[/tex]
then there is a force P acting on the mass center G
then by the first equation if ag=0
then the friction force f must be equel and opposite of p and acting at the contact point A
but then by eq3 the moment about G causes an increase in [tex]\alpha[/tex]
contradicting the kinematics equation
http://img5.imageshack.us/img5/4869/scanpic0001m.jpg
now ,obviously i got something wrong but what
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