A rolling object has a radius R and rolls with a speed v. What is its total kine

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Question: A rolling object has a radius R and rolls with a speed v. What is its total kinetic energy?

Options:

Correct Answer: (1/2)mv^2 + (1/2)Iω^2

Solution:

The total kinetic energy is the sum of translational and rotational kinetic energy: (1/2)mv^2 + (1/2)Iω^2.

A rolling object has a radius R and rolls with a speed v. What is its total kinetic energy?

A rolling object has a radius R and rolls with a speed v. What is its total kinetic energy?

Step 1: Understand that a rolling object has two types of motion: it moves forward (translational) and it spins (rotational).
Step 2: The formula for translational kinetic energy (the energy due to forward motion) is (1/2)mv^2, where m is the mass and v is the speed.
Step 3: The formula for rotational kinetic energy (the energy due to spinning) is (1/2)Iω^2, where I is the moment of inertia and ω is the angular velocity.
Step 4: To find the total kinetic energy of the rolling object, you need to add the translational and rotational kinetic energy together.
Step 5: The final formula for total kinetic energy is: Total KE = (1/2)mv^2 + (1/2)Iω^2.

Translational Kinetic Energy – The energy due to the motion of the center of mass of the object, calculated as (1/2)mv^2.
Rotational Kinetic Energy – The energy due to the rotation of the object around its axis, calculated as (1/2)Iω^2, where I is the moment of inertia and ω is the angular velocity.
Rolling Motion – The combination of translational and rotational motion, where the object rolls without slipping.