![]() ![]() The blades lose lift, and it is impossible to immediately get the blades spinning fast enough to regain it. They know, for example, that a point of no return will be reached if they allow their blades to slow below a critical angular velocity during flight. Helicopter pilots are quite familiar with rotational kinetic energy. We could, in fact, have used an expression for energy instead of a kinematic relation to solve part (b). The final rotational kinetic energy equals the work done by the torque, which confirms that the work done went into rotational kinetic energy. The net work is expressed in the equation In the last part, we can calculate the rotational kinetic energy from its expression in KE rot = 1 2 Iω 2 KE rot = 1 2 Iω 2. ![]() In the second part, we can find the final angular velocity using one of the kinematic relationships. We have enough information to calculate the torque and are given the rotation angle. To find the work, we can use the equation net W = net τ θ net W = net τ θ. (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 ) 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. In this example, we verify that the work done by the torque she exerts equals the change in rotational energy. Calculating the Work and Energy for Spinning a GrindstoneĬonsider a person who spins a large grindstone by placing her hand on its edge and exerting a force through part of a revolution as shown in Figure 10.16. ![]()
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