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Massless Rod Pendulum Let us consider a massless rod (say, a plastic straw) of length L m which can freely rotate about a fixed point O, and a mass m attached to the end of the rod as sen in Figure l. As the rod rotates there is a centripetal force exerted on the mass in the direction perpendicular to the circular path. However, this force is counteracted by the tension force in the rod itself and so the only force we need to contend with acting on the mass is that due to gravity, namely m g, where g is the acceleration due to gravity. Our convention is that both negative force and velocity are acting downward a) Ideal Pendulum We shall presume we have purchased this pendulum apparatus from the Ideal Pendulum Company and that there is no resistance to the motion, nor friction in the mechanism at O We note that even though this is untrue we shall produce a model and do a reality check on it to see if the final motion really reflects our assumptions. i) Build a differential equation model for this pendulum motion by constructing a Free Body Diagram for the mass m kg at the end of the rod and considering the External Forces tangential to the circular path of the pendulum in Newton's Second Law of Motion formu- lation. Hint: L is the length of the circular path the mass m at the cnd of thc pendulum has traveled when the arc of radians has been swept in the pendulum motion where (t) is the angle of the pendulum with the vertical line at time t s. Then mt L is the m term we need to begin our model using Newtons Second Law of Motion. We can set this force equal to the sum of the External Forces acting on the mass.

          Massless Rod Pendulum
Let us consider a massless rod (say, a plastic straw) of length L m which can freely rotate about a
fixed point O, and a mass m attached to the end of the rod as sen in Figure l. As the rod rotates
there is a centripetal force exerted on the mass in the direction perpendicular to the circular path.
However, this force is counteracted by the tension force in the rod itself and so the only force we need
to contend with acting on the mass is that due to gravity, namely m g, where g is the acceleration
due to gravity. Our convention is that both negative force and velocity are acting downward
a) Ideal Pendulum We shall presume we have purchased this pendulum apparatus from the Ideal Pendulum
Company and that there is no resistance to the motion, nor friction in the mechanism at O
We note that even though this is untrue we shall produce a model and do a reality check on it
to see if the final motion really reflects our assumptions.
i) Build a differential equation model for this pendulum motion by constructing a Free Body
Diagram for the mass m kg at the end of the rod and considering the External Forces
tangential to the circular path of the pendulum in Newton's Second Law of Motion formu- lation. Hint: L is the length of the circular path the mass m at the cnd of thc pendulum
has traveled when the arc of  radians has been swept in the pendulum motion where (t) is the angle of the pendulum with the vertical line at time t s. Then mt L is the
m   term we need to begin our model using Newtons Second Law of Motion. We can set
this force equal to the sum of the External Forces acting on the mass.

massless rod pendulum let us consider a massless rod say a plastic straw of length l m which can freely rotate about a fixed point o and a mass m attached to the end of the rod as sen in fig 75963

Added by Brendan A.

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