During a certain time interval, the angular positionof a swinging door is described by θ = 5.00 + 10.0t + 2.00t^2, where u is in radians and t is in seconds. Determine the angular position, angular speed, and angu-lar acceleration of the door (a) at t = 0 and (b) at t = 3.00 s. Answer = (a) 5.00 rad, 10.0 rad/s, 4.00 rad/s^2 (b) 53 rad, 22.0 rad/s, 4.00 rad/s^2
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.
During a certain time interval, the angular positionof a swinging door is described by θ = 5.00 + 10.0t + 2.00t^2, where u is in radians and t is in seconds. Determine the angular position, angular speed, and angu-lar acceleration of the door
(a) at t = 0 and
(b) at t = 3.00 s.
Answer =
(a) 5.00 rad, 10.0 rad/s, 4.00 rad/s^2
(b) 53 rad, 22.0 rad/s, 4.00 rad/s^2
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