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