You are pulling on a rope attached to the outer radius of a pulley with a moment of inertia I = 6.4 kg · m² as shown. The magnitude of the tension force of you on the pulley is 336.5 N. A pack of mass 23.4 kg is attached to the pulley's inner radius as shown. If the inner radius of the pulley is 0.6 m and the outer radius is 0.8 m, what is the magnitude of the linear acceleration of the pack?

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Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.