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Step Pulley

Why does the angle remain constant if either one of the pulleys rotate?

Basically, if the smaller pulley rotates by an angle theta, then why does the bigger pulley rotate by an angle theta too?

Also why is theta = (distance covered by the block)/(radius of the pulley)

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  • $\begingroup$ 'Step pulley' usually means a drum with two different diameters carved or cast in a single chunk of material. Those diameters rotate together, or not at all. $\endgroup$
    – Whit3rd
    Commented Nov 29 at 5:20
  • $\begingroup$ Two questions here. I advise separating them. Many new askers will worry about making too many posts and choose to combine all their questions in one, but usually it's the latter that is frowned on and not the former. $\endgroup$
    – stickynotememo
    Commented Nov 29 at 6:34
  • $\begingroup$ @stickynotememo Thank you for your advice. I will be sure to follow it. $\endgroup$
    – Anirudh Reddy M
    Commented Nov 30 at 15:33
  • $\begingroup$ @Whit3rd Thank you for the explanation. $\endgroup$
    – Anirudh Reddy M
    Commented Nov 30 at 15:34

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The angle remains constant because, as @Whit3rd pointed out, both pulleys appear to be mechanically connected. They cannot move independent of one another. Naturally, if two pulleys move in conjunction with one another, they'll rotate through the same angle.

As for your second question, that comes from the definition of a radian, and is only true if $\theta$ is measured in radians.

A radian subtends an arc of length $r$ if the radius of the circle is $r$. Diagram showing how a radian subtends an arc length of 1 on the unit circle So if the block is lowered by a single radius's length, each point on the circle has moved the same amount - i.e. the circle has rotated by 1 rad.

The absolute distance the block moves is not important, only the amount of radii. This is given by the formula from your diagram; $\theta=\frac{x}{r}$

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  • $\begingroup$ Thank you. I initially thought that such a rotation would be possible only if the larger pulley rotates but since both are dependent on their movements, it makes sense as to why they must rotate the same angle. Also, thank you for the explanation on the radians. I never noticed that I had lost my grasp at basic trigonometry. $\endgroup$
    – Anirudh Reddy M
    Commented Nov 30 at 15:36

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