Equations of motion for ideal pendulum and cylinder with hanging mass

[joselyn]

Help! Stuck on these 2 problems

1. Determine the motions equations of an ideal pendulum of mass m and lengh r.

2. A machine is formed by a homogenous cylinder of radio R and mass M. It rotates in its axel (frictionless). A mass by an inextensible cord (massless) is roller to cylinder. Find the motions equations.

 

[Andrew Mason]

1. Determine the motions equations of an ideal pendulum of mass m and lengh r.

This is fully explained in many texts. All you need to work out is the tangential restoring force on the pendulum mass:

$$F_{tang} = ma_{tang}$$ = tangential component of mg.

2. A machine is formed by a homogenous cylinder of radio R and mass M. It rotates in its axel (frictionless). A mass by an inextensible cord (massless) is roller to cylinder. Find the motions equations.

I am not sure I understand the problem here. Is the mass on a horizontal frictionless surface begin rolled toward the cylinder or is it rotating about the cylinder?

AM

 

[thepatientmental]

Hi there,

I am sorry to hear that you are stuck on these two problems. I can definitely try to help you with them.

For the first problem, to determine the motion equations of an ideal pendulum, we can use the equation for the period of a pendulum, which is T = 2π√(l/g), where T is the period, l is the length of the pendulum, and g is the acceleration due to gravity. From this equation, we can derive the equations for the position, velocity, and acceleration of the pendulum as a function of time.

For the second problem, to find the motion equations of the machine formed by a homogenous cylinder, we can use the equations for rotational motion, which are θ = ωt and ω = αt, where θ is the angular position, ω is the angular velocity, and α is the angular acceleration. We can also use the equation for torque, τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration.

I hope this helps you get started on solving these problems. Let me know if you need any further assistance. Good luck!