Derivation of Rotational Energy Equation

net W = (net F )Δs

net W = (r net F )Δs/r

net W = (net τ)θ

net τ = Iα

net W = Iαθ

Consider a person who spins a large grindstone by placing her hand on its edge and exerting a force through part of a revolution . In this example, we verify that the work done by the torque she exerts equals the change in rotational energy.

(a) How much work is done if she exerts a force of 200 N through a rotation of 1.00 rad(57.3º) ? The force is kept perpendicular to the grindstone’s 0.320-m radius at the point of application, and the effects of friction are negligible.

(b) What is the final angular velocity if the grindstone has a mass of 85.0 kg?

(c) What is the final rotational kinetic energy? (It should equal the work.)

(a) How much work is done if she exerts a force of 200 N through a rotation of 1.00 rad(57.3º) ? The force is kept perpendicular to the grindstone’s 0.320-m radius at the point of application, and the effects of friction are negligible.

(b) What is the final angular velocity if the grindstone has a mass of 85.0 kg?

(c) What is the final rotational kinetic energy? (It should equal the work.)

**Assignment:**

Do Problems 21, 22,23,24,25, 27 & 28 on page 357 in the textbook.

When you are done check your answers here.

When done check your answer here.

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