What is the radial acceleration of an object at a point 25 meters from the axis of rotation that has a radius and a period of .22 seconds?
period= 1/w
w= 1/.22 radians/sec
acceleration= w^2 * r
To find the radial acceleration of an object, we need to use the formula:
radial acceleration (aᵣ) = (4π²r) / T²
where:
- aᵣ is the radial acceleration
- r is the radius of the object's circular path
- T is the period of rotation
In this case, the radius (r) is given as 25 meters and the period (T) is given as 0.22 seconds. We can substitute these values into the formula to calculate the radial acceleration.
aᵣ = (4π² * 25) / (0.22)²
First, let's calculate (0.22)²:
(0.22)² = 0.0484
Next, calculate (4π² * 25):
(4π² * 25) ≈ 314.16
Now, substitute these values back into the formula:
aᵣ = 314.16 / 0.0484
To calculate this division, divide the numerator by the denominator:
aᵣ ≈ 6482.23 m/s²
Therefore, the radial acceleration of the object at a point 25 meters from the axis of rotation, with a radius and a period of 0.22 seconds, is approximately 6482.23 m/s².