What is the centripetal acceleration of an object moving on a circular path of 1.5 m if it has an acceleration of 3.5 m/s2and an angular acceleration of 1.2 rad/s2?
We can start by using the formula for centripetal acceleration:
a = v^2/r
where a is the centripetal acceleration, v is the velocity of the object, and r is the radius of the circular path.
To find v, we can use the formula for tangential acceleration:
a_t = rα
where a_t is the tangential acceleration and α is the angular acceleration.
Rearranging this formula, we get:
α = a_t/r
v = a_t/α
Substituting the given values, we get:
α = 1.2 rad/s^2
a_t = 3.5 m/s^2
r = 1.5 m
v = a_t/α = 3.5 m/s^2 / 1.2 rad/s^2 = 2.92 m/s
Finally, we can use the formula for centripetal acceleration to find a:
a = v^2/r = (2.92 m/s)^2 / 1.5 m = 5.69 m/s^2
Therefore, the centripetal acceleration of the object is 5.69 m/s^2.
To find the centripetal acceleration of an object moving on a circular path, we can use the formula:
Centripetal acceleration (ac) = radius (r) * angular acceleration (α)
Given:
Radius (r) = 1.5 m
Angular acceleration (α) = 1.2 rad/s^2
Substituting the given values into the formula, we have:
ac = r * α
ac = 1.5 m * 1.2 rad/s^2
ac = 1.8 m/s^2
Therefore, the centripetal acceleration of the object is 1.8 m/s^2.