How to Calculate Translational Velocity of a Hoop Rolling Down a Slope?
What is the translational velocity of a hoop rolling down a slope without slipping?
Translational Velocity Calculation
To determine the translational velocity of a hoop rolling down a slope without slipping, we can use the equation: v = √(2gh) Where v is the translational velocity, g is the acceleration due to gravity, and h is the vertical height of the slope. Given that the hoop starts from rest and rolls down a 30° slope, we can calculate the vertical height using trigonometry: h = sin(30°) × 10.0 m Substituting the values into the equation, we get: v = √(2 × 9.8 m/s² × sin(30°) × 10.0 m) Simplifying further: v = √30.8 m²/s² Therefore, the translational velocity of the hoop after rolling 10.0 m along the slope is approximately 5.54 m/s.Translational velocity is an important concept in physics, especially when dealing with objects rolling down slopes. In this scenario, we have a thin hoop rolling down a slope without slipping. The first step is to understand the equation for calculating translational velocity, which is v = √(2gh), where v is the translational velocity, g is the acceleration due to gravity, and h is the vertical height of the slope.
Given the parameters of the problem, including the mass of the hoop, its radius, and the angle of the slope, we can calculate the vertical height using trigonometry. By substituting the values into the equation, we can simplify and find that the translational velocity of the hoop after rolling 10.0 m along the slope is approximately 5.54 m/s.
Understanding how to calculate translational velocity in a scenario like this not only helps us solve specific problems but also deepens our understanding of the principles of physics involved. By practicing similar calculations and scenarios, you can further enhance your grasp of translational velocity and its applications in real-world situations.