An object of mass 4 kg moves around a circle of radius 6m

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 = mV² / 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 = mV² / r) with the data we extracted

F = mV² / r = (4 x 12²) / 6 = ( 4 x 144) / 6 = 576 / 6 = 96 N

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

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Source

Northwestern University