Mustang acceleration problem?

Why is centripetal acceleration different from acceleration due to gravity? (UCM problem)?

• Radius of Earth: 6371 km Period of Earth's rotation: 24 h Centripetal acceleration in UCM = v^2/r For centripetal acceleration, I received 0.033 ms^-2 I checked this answer with others and it seems correct. Why is the acceleration provided in this answer based on the Earth's radius and velocity different from the acceleration due to gravity which is 9.81ms^-2? v^2= [(2*pi*r)/T]^2 a=[(4*pi^2*r)/T^2] a=4*pi^2*6371km/24h^2 a=0.033ms^-2

• Answer:

  You did your work nearly correct, and you better be damn well glad that these numbers aren't equal. The one correction that you should make, is that the period of rotation of Earth is actually about 4 minutes less than 24 hours. 23 hrs 56 min 4 seconds to be specific. Also, you use the sphere equivalent volume averaged radius of Earth. The condition where you'd be using the full radius of Earth occurs in plane with the rotation is at the EQUATOR, which means it is more applicable to use the equatorial radius instead. But still, within these digits listed, it doesn't really matter. It is still the correct order of magnitude. If they were equal, or even comparable, we wouldn't be here discussing this question. The entire reason why you are able to perceive that you are in a gravitational field is that there is a NORMAL FORCE pushing up on you. Any other constraint force can work as well. This normal force will push outward on the person on the Earth's surface, to counteract the gravitational pull on them. NOT ALL of gravity is counteracted upon by the normal force, and the remaining net force is what causes the centripetal force. What we perceive is the constraint force. We cannot actually feel gravity, despite what you might think. If you were acted upon by true gravity alone (assume uniform gravity), you wouldn't feel any force acting on you. Your entire body would be subjected to the same force per unit mass, and thus experience the same acceleration. There is no structural force needed to prevent any body material from crashing in to any other body material. You perceive this as weightlessness, which is exactly what astronauts in orbit experience. Not a lack of a force of gravity, but a lack of the normal force to constrain against it. The centripetal acceleration of Earth is indeed a very MINOR part of our lives. That is why we think that gravity is nearly the same everywhere, because it is only within about 0.3% of its typical value, at any given surface location on Earth. What we perceive as gravity ranges from 9.76 N/kg on an equatorial mountain top to 9.83 N/kg at sea level on the poles. The corresponding TRUE GRAVITY ranges from 9.79 N/kg to 9.83 N/kg.