Question

2. A homogeneous ring with mass $m'$ and radius $R$ rotates around its fixed center $O$ with uniform angular velocity $\omega$. At point $A$ on the ring, a particle of mass $m$ is connected with a light, inextensible rope of length $l$. Both the particle and the ring move on a smooth horizontal plane. If the tension of the rope is required, list the necessary equations. (Solve it using Lagrange's equations.)

          2. A homogeneous ring with mass $m'$ and radius $R$ rotates around its
fixed center $O$ with uniform angular velocity $\omega$. At point $A$ on the ring,
a particle of mass $m$ is connected with a light, inextensible rope of length
$l$. Both the particle and the ring move on a smooth horizontal plane. If
the tension of the rope is required, list the necessary equations. (Solve it
using Lagrange's equations.)

2. A homogeneous ring with mass m' and radius R rotates around its
fixed center O with uniform angular velocity ω. At point A on the ring,
a particle of mass m is connected with a light, inextensible rope of length
l. Both the particle and the ring move on a smooth horizontal plane. If
the tension of the rope is required, list the necessary equations. (Solve it
using Lagrange's equations.)

Added by Anna C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sandeep Kumar Dhania

02/28/2022

Step 1

The position of the particle of mass m can be described by the coordinates (l*sin(θ), -l*cos(θ)). Show more…

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A homogeneous ring with mass m^(') and radius R rotates around its fixed center O with uniform angular velocity omega . At point A on the ring, a particle of mass m is connected with a light, inextensible rope of length l. Both the particle and the ring move on a smooth horizontal plane. Determine the equations neccessry to solve for the tention Supporting the motion of the attatched mass m, use legranges equations, not newtonian. 2. A homogeneous ring with mass m' and radius R rotates around its fixed center O with uniform angular velocity w. At point A on the ring. a particle of mass m is connected with a light, inextensible rope of length l. Both the particle and the ring move on a smooth horizontal plane. If the tension of the rope is required, list the necessary equations. (Solve it using Lagrange's equations.) om x m