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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

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

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter10: Rotational Motion
Section: Chapter Questions
Problem 16P: Figure P10.16 shows the drive train of a bicycle that has wheels 67.3 cm in diameter and pedal...
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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° Arm Number i Units
Transcribed Image Text: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° Arm Number i Units
Expert Solution
Step 1

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 Fc = mrω2, where

m = mass of the body,

r = radius of rotation and

ω = angular velocity of the body.

The angular velocity of a body is given by ω = 2πT, where

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

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