What Determines the Acceleration Direction in Pendulum Motion?

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AI Thread Summary
The discussion focuses on determining the direction of acceleration for a pendulum at specific moments in its motion. The pendulum is released from a 45-degree angle, and participants are trying to resolve the weight into components to identify acceleration direction. At moment 0, the weight acts downward, and one component points away from the center of rotation. The conversation emphasizes the importance of understanding circular motion and the relationship between velocity and acceleration. Overall, the participants seek guidance on resolving forces to clarify the pendulum's acceleration direction.
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Homework Statement



The motion diagram shown in the figure represents a pendulum released from rest at an angle of 45 from the vertical. The dots in the motion diagram represent the positions of the pendulum bob at eleven moments separated by equal time intervals. The green arrows represent the average velocity between adjacent dots. Also given is a "compass rose" in which directions are labeled with the letters of the alphabet.

pendulum.jpg

Note: The letters in the diagram correspond to the directions.

How can I find the direction of the acceleration of the object at moments 0 and 10?


2. Relevant topics

Circular Motion
Acceleration and direction of object in motion



The Attempt at a Solution



First of all, I am having trouble find the velocity of said moments. Can someone help with this?
 
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resolve the weight into components when it is at an angle θ. One should point in the towards the center.
 
Anymore tips?
Still can't figure it out. :/
 
Lemniscate said:
Anymore tips?
Still can't figure it out. :/

ok at point 0, draw the weight downwards. Resolve the weight now. One component points away from the centre of rotation.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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