A circular space station with a radius of 72 m has just been completed. In order to provide astronauts with the feeling of gravity, the space station will be set spinning about its central axis. To do this, solid fuel rockets have been attached around the perimeter of this station to start it spinning. These rockets fizzle out quickly, and produce a non-uniform angular acceleration of =a0e−bt Where a0 = 0.0424 rad/s2 and b = 0.153 s-1. The station is at rest (is not spinning) when the rockets are ignited at t = 0 s. What is the tangential speed of the outer edge of the station about the center of the station at t = 6.27 s? Through what angle has the station rotated in that time? Once the rockets are done burning, how long does it take the station to complete one revolution?
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.
A circular space station with a radius of 72 m has just been completed. In order to provide astronauts with the feeling of gravity, the space station will be set spinning about its central axis. To do this, solid fuel rockets have been attached around the perimeter of this station to start it spinning. These rockets fizzle out quickly, and produce a non-uniform
=a0e−bt
Where a0 = 0.0424 rad/s2 and b = 0.153 s-1. The station is at rest (is not spinning) when the rockets are ignited at t = 0 s.
What is the tangential speed of the outer edge of the station about the center of the station at t = 6.27 s?
Through what angle has the station rotated in that time?
Once the rockets are done burning, how long does it take the station to complete one revolution?
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