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

Answer 1

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.