Answer:
The total linear acceleration is approximately 0.246 meters per square second.
Explanation:
The total linear acceleration () consist in two components, <em>radial</em> (
) and <em>tangential</em> (
), in meters per square second:
(1)
(2)
Since both components are orthogonal to each other, the total linear acceleration is determined by Pythagorean Theorem:
(3)
Where:
- Radius of the wheel, in meters.
- Angular speed, in radians per second.
- Angular acceleration, in radians per square second.
Given that wheel accelerates uniformly, we use the following kinematic equation:
(4)
Where:
- Initial angular speed, in radians per second.
- Time, in seconds.
If we know that ,
,
and
, then the total linear acceleration is:
The total linear acceleration is approximately 0.246 meters per square second.