A rotating wheel has an angular momentum of 10 kg·m²/s. If its moment of inertia
Practice Questions
Q1
A rotating wheel has an angular momentum of 10 kg·m²/s. If its moment of inertia is 2 kg·m², what is its angular velocity?
5 rad/s
10 rad/s
20 rad/s
2 rad/s
Questions & Step-by-Step Solutions
A rotating wheel has an angular momentum of 10 kg·m²/s. If its moment of inertia is 2 kg·m², what is its angular velocity?
Correct Answer: 5 rad/s
Step 1: Understand the formula for angular momentum, which is L = Iω, where L is angular momentum, I is moment of inertia, and ω is angular velocity.
Step 2: Identify the values given in the question: L (angular momentum) is 10 kg·m²/s and I (moment of inertia) is 2 kg·m².
Step 3: Rearrange the formula to solve for angular velocity (ω). The rearranged formula is ω = L/I.
Step 4: Substitute the values into the formula: ω = 10 kg·m²/s ÷ 2 kg·m².
Step 5: Perform the division: 10 ÷ 2 = 5.
Step 6: Conclude that the angular velocity (ω) is 5 rad/s.
Angular Momentum – Angular momentum (L) is the product of a body's moment of inertia (I) and its angular velocity (ω), expressed as L = Iω.
Moment of Inertia – Moment of inertia (I) is a measure of an object's resistance to changes in its rotation, depending on the mass distribution relative to the axis of rotation.
Angular Velocity – Angular velocity (ω) is the rate of change of angular position of a rotating body, typically measured in radians per second.
