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

Question

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

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