A tire (R = 0.5 m) starts from rest and accelerates at 40 m/s? for 8 s. a) What is the total angular displacement? b) What is the velocity of the tire at 8 seconds? c) What is the angular acceleration?
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.
Angular displacement formula is given by:
Where is the initial velocity, is the angular acceleration, and is time.
Angular velocity is the rate of change of angular displacement and can be described by the relationship:
Where is the change in displacement, and is the change in time.
Angular acceleration formula is as follows:
Where is angular acceleration, is the change in angular velocity, is change in time, is initial and final angular velocity respectively, and is initial and final time respectively.
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