IB Physics Mass on the end of a Swinging Rod
/A tutorial sheet on the problem of a mass on the end of a uniform rod swinging in a vertical plane. A question answered correctly by only a small percentage of the world.
A uniform rod of mass 2m and length L has a particle of mass m attached to its lower end. The rod is free to swing in a vertical plane about a horizontal axis through its upper end. The rod is released from rest at the horizontal.
- Draw a free-body diagram showing the forces acting on the (i) particle, (ii) rod. The rod exerts an inwards force Y acting along the rod and a perpendicular force Y on the particle inwards along the tangent to the circular path. This question involves a rod and not a string. For a string Y=0.
- Use Newton's second law in terms of forces to write down the two equations of motion of the particle. The equations are written in terms of components parallel to the rod and perpendicular to the rod.
- Use Newton's second law for rotational motion to write down the equation of motion for the system in terms of the net torque acting on it.
- Solve the three equations simultaneously to find the force components exerted by the rod on the particle.
- Show that X = mgsin𝜃/5 and Y = 17mgcos𝜃/5, where 𝜃 is the angle made by the rod with the vertical.
- The force exerted by the rod on the particle is directed towards the centre of the circle only when the rod is vertical (𝜃=0°).
