Adhesive capsulitis, also known as a "frozen shoulder" is a condition that affects the motion of the shoulder joint. The articular shoulder capsule becomes inflamed, stiff, and restricts a person's mobility. Physical therapy provides one course of treatment for a frozen shoulder. One of the exercises often performed is the pendulum. Here, the patient bends forward and lets the injured arm hang downward and swing freely like a pendulum (see figure). The patient slowly swings their arm in a circular motion, for say 10 cycles, and then switches direction and completes 10 more. The patient may hold a light-weight dumbbell while performing this motion, or just use an empty hand. Imagine the situation shown in the drawing. A patient is moving a 7.0- Ib (3.2 kg) dumbbell at constant speed and completes one circular motion in 1.2 s. What is the radius (r) of the circular motion? 47°i Arm Number i Units

We first take the freebody diagram of the weight and draw the centripetal forces, force F in the arm, the weight.

We equate the forces in the X and Y directions to find the radius.

The centripetal force acting on a body rotating at a certain radius is given by $F_c = mr{\omega }^2$, where

m = mass of the body,

r = radius of rotation and

$\omega$ = angular velocity of the body.

The angular velocity of a body is given by $\omega = \frac{2\pi }{T}$, where

T is the Time period or time the body takes to complete one rotation.