a body moves along a circular path with uniform angular speed of 6 rads per second and at a constant speed of 30m/s,calculate the acceleration of the body towards the center of the circle
The acceleration of an object moving in a circular path is given by the formula:
a = v^2 / r
where:
a = acceleration
v = speed of the object
r = radius of the circle
In this case, the speed of the object is 30 m/s and the radius of the circle is not given. However, we can calculate the radius using the angular speed:
ω = 2π/T
6 = 2π/T
T = 2π / 6
T = π / 3 seconds
Now, the radius of the circle is given by:
v = ω * r
30 = 6 * r
r = 30 / 6
r = 5 meters
Substitute the values into the formula:
a = (30)^2 / 5
a = 900 / 5
a = 180 m/s^2
Therefore, the acceleration of the body towards the center of the circle is 180 m/s^2.