## Question

A stone of mass 500g tied to a rope 50 cm long is whirled at an angular velocity of 12.0 radians per second. Calculate the centripetal force.

## Answer

**The central force of the stone is 36 Newtons**

### Explanation

**Data: Unrevealed information from the question **

Mass of the stone, m = 500 g = (500 / 1000) kg = 0.5 kg

Radius of the circle, r = 50 cm = (50 / 100) m = 0.5 m

Angular velocity, ω = 12 rad/s

**Unknown: Unrevealed information from the question **

Linear velocity, V = ?

Centripetal force, F = ?

**Formula: The equation that will help us solve the problem**

**Step 1:** To find the linear velocity, we will apply the equation below

**V = ωr**

**Step 2:** We can use the formulae below to calculate the centripetal force

**F = mV ^{2} / r** and since

**V = ωr**

We can say that **F = mω ^{2}r** [Which is the formula that will help us find the centripetal force]

#### Solution

**Step 1:** If we are to use the first formula, we will start by by finding the linear velocity

**V = ωr** = 12 x 0.5 = 6 m/s

**Therefore, the linear velocity of the stone is 6 m/s**

**Step 2:** We will now apply the formula ** F = mω^{2}r** to find the centripetal force

Hence,

**F = mω ^{2}r** = 0.5 x 12

^{2}x 0.5 = 0.5 x 144 x 0.5 = 36 N

**Therefore, the centripetal force is 36 Newtons **

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