A sphere rolls on a flat surface with a speed v. What is the kinetic energy of t
Practice Questions
Q1
A sphere rolls on a flat surface with a speed v. What is the kinetic energy of the sphere?
(1/2)mv^2
(1/2)mv^2 + (1/5)mv^2
(1/2)mv^2 + (2/5)mv^2
(1/2)mv^2 + (3/5)mv^2
Questions & Step-by-Step Solutions
A sphere rolls on a flat surface with a speed v. What is the kinetic energy of the sphere?
Step 1: Understand that a sphere rolling on a flat surface has two types of motion: it moves forward (translational motion) and it spins (rotational motion).
Step 2: The formula for translational kinetic energy (the energy due to forward motion) is (1/2)mv^2, where m is the mass of the sphere and v is its speed.
Step 3: The formula for rotational kinetic energy (the energy due to spinning) for a solid sphere is (2/5)mv^2.
Step 4: To find the total kinetic energy of the rolling sphere, add the translational kinetic energy and the rotational kinetic energy together.
Step 5: The total kinetic energy is (1/2)mv^2 + (2/5)mv^2.
Translational Kinetic Energy – The energy due to the motion of the center of mass of the sphere, calculated as (1/2)mv^2.
Rotational Kinetic Energy – The energy due to the rotation of the sphere about its center of mass, calculated as (1/2)Iω^2, where I is the moment of inertia and ω is the angular velocity.
Moment of Inertia – For a solid sphere, the moment of inertia I is (2/5)mr^2, which is used to calculate the rotational kinetic energy.
Rolling Motion – Understanding the relationship between translational and rotational motion in rolling objects.
