A planet orbits the sun in a circular path. If the radius of the orbit is halved
Practice Questions
Q1
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?
It doubles
It halves
It remains the same
It becomes zero
Questions & Step-by-Step Solutions
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.
