A stone of mass 500g tied to a rope 50 cm long

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.

The central force of the stone is 36 Newtons

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 = mV² / r and since V = ωr

We can say that F = mω²r [Which is the formula that will help us find the centripetal force]

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 = mω²r to find the centripetal force

Hence,

F = mω²r = 0.5 x 12² x 0.5 = 0.5 x 144 x 0.5 = 36 N

Therefore, the centripetal force is 36 Newtons

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