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?

A cube, whose mass is 0.700 kg, is attached to a spring with a force constant of 110 N/m. The cube rests upon a frictionless, horizontal surface (shown in the figure below). A cube labeled m is attached to the right end of a horizontal spring, and the left end of the spring is attached to a wall. The spring is stretched horizontally such that the cube is displaced by a distance A to the right of its equilibrium position. The cube is pulled to the right a distance A = 0.110 m from its equilibrium position (the vertical dashed line) and held motionless. The cube is then released from rest. (a) At the instant of release, what is the magnitude of the spring force (in N) acting upon the cube?  N (b) At that very instant, what is the magnitude of the cube's acceleration (in m/s2)?  m/s2 (c) In what direction does the acceleration vector point at the instant of release?

A small ball is attached to one end of a spring that has an unstrained length of 0.185 m. The spring is held by the other end, and the ball is whirled around in a horizontal circle at a speed of 4.80 m/s. The spring remains nearly parallel to the ground during the motion and is observed to stretch by 0.0190 m. By how much would the spring stretch if it were attached to the ceiling and the ball allowed to hang straight down, motionless? Number Units

Students work together during an experiment about Newton’s laws.  The students use a setup that consists of a cart of known mass connected to one end of a string that is looped over a pulley of negligible friction, with its other end connected to a hanging mass.  The cart is initially at rest on a horizontal surface and rolls without slipping when released.  The inertia of the cart's wheels is negligible.  Students have access to common laboratory equipment to make measurements of components of the system.   By collecting the appropriate data, the students can determine the relationship between the acceleration of the cart and the net force exerted on the cart.  Which of the following graphs should the students produce to show the correct relationship?      a A  b C  c D  d B