Question
A body moves along a circular path with uniform angular speed of 0.6 rad/s. and at a constant speed of 3.0 meters per second. Calculate the acceleration of the body towards the center of the circle.
Answer
The final answer to this question (acceleration of the body towards the center of the circle) is 1.8 ms-2.
Explanation
Data: Revealed information from the question
Angular velocity, ω = 0.6 rad/s
Linear velocity, V = 3.0 m/s
Unknown: Unrevealed information from the question
Radius of the circle, r = ?
Centripetal acceleration, a = ?
Formula: The equation that will help us solve the problem
Step 1: To find the radius of the circle, we will apply the equation below
r = V/ω [ Because V = ωr]
Step 2: We can use the formulae below to calculate the centripetal force
a = V2 / r
Solution
Step 1: To calculate the radius of the circle, i will the formula
r = V/ω = 3 / 0.6 = 5 m
Therefore, the radius of the circle is 5 meters
Step 2: By applying the formula a = V2 / r, we can find the centripetal acceleration as
a = V2 / r = 32 / 5 = 9 / 5 = 1.8 m/s2
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