## Question

An object of mass 4 kg moves around a circle of radius 6m with a constant speed of 12 meters per second. Calculate the angular speed and the force toward the center

### Answer

**The final answer to this question is that the angular speed (ω) is 2 radians per second, and the centripetal force is 96 Newtons**.

#### Explanation

**Data: Revealed information from the question**

Mass of the object, m = 4 kg

The radius of the circle, r = 6 m

Constant speed, V = 12 m/s

**Unknown: Unrevealed information from the question**

Angular speed, ω = ?

Centripetal force, F = ?

**Formula: The equations that will help us solve the problems**

**Step 1:** We will apply the formula below to find the angular speed

ω = V / r

**Step 2:** We will also calculate centripetal force by using the formula

F = mV^{2} / r

##### Solution

**Step 1:** We will now start by inserting our data into the formula ω = V / r to calculate the angular speed

ω = V / r = 12 / 6 = 2 rad/s

**Therefore, the angular velocity is 2 radians per second**

**Step 2:** Substitute your formula (F = mV^{2} / r) with the data we extracted

F = mV^{2} / r = (4 x 12^{2}) / 6 = ( 4 x 144) / 6 = 576 / 6 = **96 N**

**Therefore, the force towards the center (centripetal force) is 96 Newtons**.

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