A planet orbits the sun in a circular path. If the radius of the orbit is double
Practice Questions
Q1
A planet orbits the sun in a circular path. If the radius of the orbit is doubled, what happens to the angular momentum of the planet if its speed remains constant?
Doubles
Halves
Remains the same
Quadruples
Questions & Step-by-Step Solutions
A planet orbits the sun in a circular path. If the radius of the orbit is doubled, what happens to the angular momentum of the planet if its speed remains constant?
Step 1: Understand what angular momentum is. Angular momentum (L) is calculated using the formula L = mvr, where m is mass, v is speed, and r is the radius of the orbit.
Step 2: Identify the variables in the formula. In this case, we have mass (m), speed (v), and radius (r).
Step 3: Note the condition given in the question. The radius of the orbit is doubled, which means r becomes 2r.
Step 4: Recognize that the speed (v) remains constant. This means that v does not change.
Step 5: Substitute the new radius into the angular momentum formula. The new angular momentum L' will be L' = m * v * (2r).
Step 6: Simplify the new angular momentum. L' = 2 * (m * v * r) = 2L, where L is the original angular momentum.
Step 7: Conclude that if the radius is doubled and the speed remains constant, the angular momentum also doubles.
Angular Momentum – Angular momentum (L) is defined as the product of the mass (m), velocity (v), and radius (r) of the orbit (L = mvr).
Conservation of Angular Momentum – In a closed system, if no external torque acts on the object, angular momentum is conserved.
Effect of Radius on Angular Momentum – If the radius of the orbit increases while speed remains constant, angular momentum increases proportionally to the radius.
