If you have a 5 inch grinding wheel with 5000 rpms and a piece off material lies off of it how fast is the material moving?
The tangential speed is given by the radius times the angular speed.
Vf= r*w= 2.5inch*5000rev/min*2PIrad/rev
Vf= 2.5*5000*2PI inches/min*1min/sec
Vf=2.5*5000*2PI*60 inches/second
can you break this into english for me my son asked me and im not sure how to explain
To determine the speed at which the material is moving, we need to calculate the linear velocity of the grinding wheel's edge. Here's how you can do it:
1. First, convert the diameter of the grinding wheel from inches to feet. Since 1 foot is equal to 12 inches, divide the diameter of 5 inches by 12 to get the diameter in feet: 5 / 12 = 0.4167 feet.
2. Next, calculate the circumference of the grinding wheel. The circumference of a circle is given by the formula C = π * d, where C is the circumference and d is the diameter. Use the formula and the converted diameter to find the circumference: C = π * 0.4167 = 1.309 ft.
3. Now, we can calculate the linear velocity of the grinding wheel using the formula v = ω * r, where v is the linear velocity, ω is the angular velocity in radians per second, and r is the radius of the grinding wheel. The radius is half the diameter, so the radius of the grinding wheel is 0.2083 ft (0.4167 / 2).
4. The angular velocity is given as 5000 revolutions per minute (rpm). To convert it to radians per second (rad/s), multiply by 2π/60: ω = (5000 * 2π) / 60.
5. Substitute the values into the formula: v = (5000 * 2π / 60) * 0.2083 ≈ 547.35 ft/s.
Therefore, the material lying off the 5-inch grinding wheel would be moving at a speed of approximately 547.35 ft/s.