Question

A constant torque of 24.5 N · m is applied to a grindstone whose moment of inertia is 0.130 kg · m2. Using energy principles, and neglecting friction, find the angular speed after the grindstone has made 16.9 revolutions. Hint: the angular equivalent of Wnet = FΔx = 1 2 mvf2 − 1 2 mvi2 is Wnet = τΔθ = 1 2 Iωf2 − 1 2 Iωi2. You should convince yourself that this last relationship is correct. (Assume the grindstone starts from rest.)

Answer 1

To find the final angular speed of the grindstone after it has made 16.9 revolutions, we can use energy principles and the equation τΔθ = 1/2Iωf² - 1/2Iωi².

Step-by-step explanation:

To find the final angular speed of the grindstone after it has made 16.9 revolutions, we can use the energy principles. The work done on an object is equal to the change in its rotational kinetic energy. In this case, the work done on the grindstone is equal to the change in its rotational kinetic energy.

Using the equation τΔθ = 1/2Iωf² - 1/2Iωi², where τ is the torque, Δθ is the change in angle (in radians), I is the moment of inertia, ωf is the final angular velocity, and ωi is the initial angular velocity.

Since the grindstone starts from rest, the initial angular velocity is 0. We can rearrange the equation to solve for ωf: ωf = √(2τΔθ/I)