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SHM · Lecture 15 of 26

Pulleys with springs, and springs at an angle

By Lalit, IIT Madras

Pulleys with springs, JEE Advanced SHM: k effective from the string constraint, a pulley with mass, and a rolling disc tied to a spring.

Watch lecture 15

Chalkboard titled "Two slanted springs": a mass m is joined to a wall on its left by a horizontal spring k and pulled on its right by two slanted springs at angle θ0 above and below the line, with the boxed formulas k effective = k(1 + 2 cos²θ0) and T = 2π√(m/(k effective)).

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What this lecture covers

Hung on a spring, a light pulley sets the pattern: the string constraint links its displacement to the block's, the massless pulley carries zero net force, and k effective follows. Hanging the block from a pulley with a spring on the string works the same way. Giving the pulley mass brings in torque. For a disc tied to a spring and rolling without slipping, torques are taken about the centre and then about the contact point. Slanted springs come last.

In this lecture

  1. Play from A light pulley on a spring
  2. Play from The string constraint sets k effective
  3. Play from A hanging block, spring on the string
  4. Play from A massive pulley: tensions and torque
  5. Play from A rolling body tied to a spring
  6. Play from The second route: the contact point
  7. Play from A mass held by springs at angles
  8. Play from The stretch of a slanted spring
  9. Play from A line spring and two slanted springs
  10. Play from Recap: pulleys, rolling and angles