If a rolling object has a mass m and radius r, what is the expression for its to

If a rolling object has a mass m and radius r, what is the expression for its total kinetic energy?

If a rolling object has a mass m and radius r, what is the expression for its total kinetic energy?

Step 1: Understand that a rolling object has two types of motion: it moves forward (translational motion) and it spins (rotational motion).
Step 2: The translational kinetic energy (TKE) is given by the formula (1/2)mv^2, where m is the mass and v is the linear velocity of the object.
Step 3: The rotational kinetic energy (RKE) is given by the formula (1/2)Iω^2, where I is the moment of inertia and ω is the angular velocity.
Step 4: For a solid sphere or cylinder, the moment of inertia I can be expressed as (2/5)mr^2, where r is the radius of the object.
Step 5: Substitute the moment of inertia into the rotational kinetic energy formula: RKE = (1/2)(2/5)mr^2(ω^2).
Step 6: Combine the translational and rotational kinetic energy to find the total kinetic energy: Total KE = TKE + RKE.
Step 7: Write the final expression for total kinetic energy: Total KE = (1/2)mv^2 + (1/2)(2/5)mr^2(ω^2).

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