A large disc-shaped grindstone is spinning at 500 revolutions/min. The grindstone has a mass 4.0 kg and radius 9.0 cm. The moment of inertia of a disc rotating about its center is given by I = // MR² The power is shut off by the operator and to slow it down, she sharpens a 4 kg axe by holding it against the grindstone until it stops 7 s later. Assume the angular acceleration is constant while the grindstone is slowing down. (A) Draw a diagram which shows the edge of the axe exerting a frictional torque on the large grindstone. Indicate the direction of rotation of the grindstone with an arrow. Then label the direction of the angular velocity (w) and the direction of the torque supplied by the axe (7) each with arrows. (B) Write relevant symbolic equation(s) which would provide a way to solve for angular acceleration and torque. Then solve these equations symbolically for torque exerted by the axe on the grindstone in terms of, the initial angular velocity (w), time it takes for the rotation to stop (t), the mass of the grindstone (m), the radius of the grindstone (r) and any needed constants. (C) Solve for the magnitude of the angular acceleration and the net frictional torque exerted by the axe on the grindstone.
A large disc-shaped grindstone is spinning at 500 revolutions/min. The grindstone has a mass 4.0 kg and radius 9.0 cm. The moment of inertia of a disc rotating about its center is given by I = // MR² The power is shut off by the operator and to slow it down, she sharpens a 4 kg axe by holding it against the grindstone until it stops 7 s later. Assume the angular acceleration is constant while the grindstone is slowing down. (A) Draw a diagram which shows the edge of the axe exerting a frictional torque on the large grindstone. Indicate the direction of rotation of the grindstone with an arrow. Then label the direction of the angular velocity (w) and the direction of the torque supplied by the axe (7) each with arrows. (B) Write relevant symbolic equation(s) which would provide a way to solve for angular acceleration and torque. Then solve these equations symbolically for torque exerted by the axe on the grindstone in terms of, the initial angular velocity (w), time it takes for the rotation to stop (t), the mass of the grindstone (m), the radius of the grindstone (r) and any needed constants. (C) Solve for the magnitude of the angular acceleration and the net frictional torque exerted by the axe on the grindstone.
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