- #1
Shoelace Thm.
- 60
- 0
Suppose I have a hinged meter stick of length [itex] L [/itex] and mass [itex] M [/itex] angled at angle [itex] \theta [/itex], where one end is free to rotate while the other end serves as a rotation axis. There is a ball sitting on a golf tee at the edge and a cup sitting [itex] L \cos \theta [/itex] up the ramp. As the stick falls, its free end starts to accelerate above gravity (though that is not necessarily the case when it starts!)
I have that [itex] \ddot{\theta} =\frac{3g}{2l} \cos \theta [/itex] but how can I get [itex] \theta [/itex] as a function of [itex] t [/itex]? The goal is to eventually find the critical angle where the cup reaches the ground right before the ball.
Of course, if there is an easier way to find this critical angle, please let me know.
I have that [itex] \ddot{\theta} =\frac{3g}{2l} \cos \theta [/itex] but how can I get [itex] \theta [/itex] as a function of [itex] t [/itex]? The goal is to eventually find the critical angle where the cup reaches the ground right before the ball.
Of course, if there is an easier way to find this critical angle, please let me know.
Last edited: