## 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 = V ^{2} / 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 = V ^{2} / r**, we can find the centripetal acceleration as

a = V^{2} / r = 3^{2} / 5 = 9 / 5 = 1.8 m/s^{2}

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