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Suppose there is a pendulum with a centre of mass half the way up the rod. Will the centre of mass accelerate at g, meaning the end accelerates faster?

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  • $\begingroup$ note: there is a difference between linear acceleration (which shouldn't be constant) and angular acceleration $\endgroup$ Jan 18, 2018 at 9:41

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There are two things you have to understand here. One is that if the pendulum blob is a rigid body than it has same angular acceleration because if all the parts of the pendulum didn’t move through the same angles then the pendulum would no longer be a rigid body. Also, you are right that the end indeed has greater linear acceleration as linear acceleration,$a$: $$a=\alpha r$$ where $\alpha$ is angular acceleration so as the end has greater distance,$r$ from axis of rotation it has greater linear acceleration.

One other thing I need to clarify is that the acceleration of a pendulum is not $g$ it is rather $gsin(\theta)$ where $\theta$ is the angle of the pendulum with the vertical; because if you draw a free-body diagram you’ll see that only resultant force on the pendulum(without air resistance) is the component of gravity perpendicular to the string.

Note: When a pendulum swings the angle $\theta$ changes and so the angular and linear acceleration also changes but it’s right to assume that the end parts have higher linear acceleration but all parts have same angular acceleration at each point in time.

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