Integrated Concepts You have a grindstone (a disk) that is 90.0 kg, has a 0.340-m radius, and is turning at 90.0 rpm, and you press a steel axe against it with a radial force of 20.0 N. (a) Assuming the kinetic coefficient of friction between steel and stone is 0.20, calculate the angular acceleration of the grindstone. (b) How many turns will the stone make before coming to rest?
Step-by-step solution Step 1 o f 13 The force of kinetic friction acting on the surface is, Where is the friction force, is the coefficient of friction and is the normal force due to the axe on the grinder. Step 2 o f 13 (a) Use the above formula, Step 3 o f 13 Substitute 0.20 for and for . Step 4 o f 13 This frictional force is reducing the speed of the grindstone, so the angular acceleration will be negative. As the radius of the grindstone is 0.340-m, so the torque due to this frictional force about the axis is Here is the torque, is the radius of the grindstone, is the frictional force acting on the surface. Step 5 o f 13 Substitute the values of for and for in the above equation. Step 6 o f 13 Also, the formula to find the torque acting on the grindstone is, Here is the moment of inertia of the grindstone, is the angular acceleration the grindstone around its axis of rotation. Step 7 o f 13 The moment of inertia of the grindstone (disk) is, Here is the mass of the grindstone and is the radius.