A planet orbits the sun in a circular path. If the radius of the orbit is halved

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Question: A planet orbits the sun in a circular path. If the radius of the orbit is halved, what happens to the angular momentum of the planet?

Options:

Correct Answer: It halves

Solution:

Angular momentum L = mvr; if the radius is halved and speed remains constant, angular momentum halves.

A planet orbits the sun in a circular path. If the radius of the orbit is halved, what happens to the angular momentum of the planet?

A planet orbits the sun in a circular path. If the radius of the orbit is halved, what happens to the angular momentum of the planet?

Step 1: Understand what angular momentum is. Angular momentum (L) is calculated using the formula L = mvr, where m is mass, v is velocity (speed), and r is the radius of the orbit.
Step 2: Identify the initial conditions. The planet has a certain mass (m), a certain speed (v), and a radius (r) for its orbit around the sun.
Step 3: Recognize what happens when the radius is halved. If the radius (r) is changed to r/2, we need to see how this affects angular momentum.
Step 4: Substitute the new radius into the angular momentum formula. The new angular momentum becomes L' = m * v * (r/2).
Step 5: Simplify the new angular momentum formula. L' = (m * v * r) / 2, which means L' = L / 2, where L is the original angular momentum.
Step 6: Conclude that if the radius is halved and the speed remains constant, the angular momentum of the planet also halves.

Angular Momentum – Angular momentum (L) is the product of an object's mass (m), its velocity (v), and the radius (r) of its circular path, expressed as L = mvr.
Effect of Radius on Angular Momentum – Halving the radius while keeping the speed constant results in a direct halving of angular momentum, as L is directly proportional to r.