Determine Centripetal Acceleration acting on the person standing at the equator? (the radius of earth is given)
To determine the centripetal acceleration acting on a person standing at the equator, we need to use the formula for centripetal acceleration:
\[ a_c = \frac{{v^2}}{{r}} \]
Where:
- \( a_c \) is the centripetal acceleration
- \( v \) is the linear velocity of the object
- \( r \) is the radius of the circular path
In this case, the linear velocity of the person at the equator can be calculated using the equation:
\[ v = \omega \times r \]
Where:
- \( \omega \) is the angular velocity of the Earth's rotation
The angular velocity of the Earth's rotation is constant and is given by:
\[ \omega = \frac{{2\pi}}{{T}} \]
Where:
- \( T \) is the period of rotation of the Earth (24 hours)
Once we have the linear velocity, we can substitute it back into the formula for centripetal acceleration to find the answer. Let's do the calculations step by step.
First, we need to find the angular velocity:
\[ \omega = \frac{{2\pi}}{{T}} = \frac{{2\pi}}{{24 \times 60 \times 60}} \, \text{rad/s} \]
Next, calculate the linear velocity:
\[ v = \omega \times r \]
Finally, plug the values into the centripetal acceleration formula:
\[ a_c = \frac{{v^2}}{{r}} \]
Substituting in the values will give us the answer.
To determine the centripetal acceleration acting on a person standing at the equator, you need to consider the rotational motion of the Earth.
The centripetal acceleration is given by the equation:
a = ω²r
Where:
a is the centripetal acceleration,
ω (omega) is the angular velocity,
r is the radius.
First, find the angular velocity of the Earth:
The Earth makes a complete revolution in 24 hours, or 86400 seconds. The angular velocity (ω) can be calculated as the angle through which the Earth moves divided by the time taken to complete the motion.
ω = 2π / T
Where:
T is the period, which is 86400 seconds.
ω = 2π / 86400
Next, you need to determine the radius of the Earth. The average radius of the Earth is about 6,371 kilometers or 6,371,000 meters.
Now plug in the values into the centripetal acceleration formula:
a = (2π / 86400)² * 6,371,000
Calculating this formula will give you the centripetal acceleration acting on a person at the equator.