I got this question as my physics class homework for tomorrow. Anyone please help me out.
If Earth constantly rotates and revolves, then how can we call an object in a state of rest?
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"A state of rest" is a relative term. Relative means - measured in comparison to the things around it.
When you sit in a train and sip from a cup of coffee, you can do so because the cup is still relative to you even though both of you might be hurtling through the countryside at 200 km/h.
For most experiments, objects can be considered "at rest" if they don't move relative to the things around them. But the "frame of reference" (the thing that you consider "stationary") does matter.
For example - if you sit in a car that accelerates, you might be "at rest" relative to the car, but you can feel yourself being pushed into the seat of the car by an invisible force. Similarly, there are measurable effects on earth that are due to the fact that Earth rotates about its axis (for example - the way air rotates around a low pressure region is a consequence of the rotation of the Earth), and even effects that relate to the motion around the sun (including the tides).
Physicists call accelerating and rotating frames of reference "non-inertial", and say that observations in such frames "give rise to fictitious forces" - that is, if you think your non-inertial frame is stationary, you will also think that a force has appeared out of thin air. Such as the force that pushes you into the seat of the accelerating car. Or the "force" that makes you spill your drink when the car goes over a bump (and your "frame of reference" suddenly accelerates).
But for many "in classroom" experiments, we can ignore all these things. Much of physics (and science) is about knowing what you can ignore, and when you can ignore it.
Revolving around the sun is equivalent to free fall around the sun, so the revolution allows you not to 'feel' the sun's gravity.
The rotation of the earth is something that can be measured: (i) a centrifugal force which is a small offset on gravity, and (ii) causes the coriolis force. Both these are small effects, so can often be ignored for laboratory experiments.
"Rest, in physics, refers to an object being stationary relative to a particular frame of reference or another object." - Wikipedia (emphasis mine)
While on Earth, the planet is often treated as the default frame of reference. It is not a perfect frame of reference, but for many purposes it is good enough. Since there is no absolute frame of reference, some frame of reference must be chosen, and for us earth-dewllers the frame defined by the earth itself is familiar and often easy to work with. Being a non-inertial frame there are some fictitious forces that may need to be accounted for, but for many purposes those forces are negligible and when they're not we have well established methods to account for them.
Whenever a frame of reference is not specified, it is usually expected that you will assume a frame of reference that matches the assumptions used in similar exercises or in discussions preceding the exercises. The two sets of assumptions I have seen most often are
"As-on-earth", assuming fictitious forces are negligible, ignoring surface curvature & air resistance, and assuming a constant gravitational field, and
An abstract inertial frame with no gravity or atmosphere.
Both are often confined to 2 dimensions. If you're not sure, you can usually ask for clarification, or give multiple answers for different frames.
Solving lots of physics problems involved you choosing a frame of reference. As long as all your formulations are from a particular frame of reference, for example the energy of objects then the laws will work. Since you are also travelling with the object, (as the earth rotates) it is easier to say you are at rest. If you are travelling at constant velocity relative to something at rest, the physics will work if you consider you are at rest and the other thing is travelling at constant velocity.
When you're in a moving vehicle and see trees or buildings, who is moving? Are you moving forward, or are the trees and buildings moving backward? Its counter-intuitive for beginners but both these views are absolutely correct.
We can only describe the motion of an object from a reference frame. A reference frame is a specific configuration from where you can observe/describe the system. The earth indeed is moving, but the objects on it are moving along with it too, and hence with respect to the Earth, the objects are at rest. (i.e. they move with the same velocity as the Earth.) (e.g. an object which is stationary with respect to you is not stationary when observed by someone moving by!)
An object's relative velocity w.r.t you determines whether it is at rest with respect to you or not. If there are two objects $A$ and $B$ (with velocities $V_A,V_B$), the relative velocity of $A$ with respect to $B$ is $$V_B-V_A$$
This is zero if $A$ and $B$ are at rest with respect to each other.