Final answer:
To find the centripetal acceleration and linear speed of a grindstone, use the formulae for centripetal acceleration and linear speed with the given radius and angular velocity. Visual inspections, ring tests, and vibrations analysis are common methods for checking grinding wheel safety. Similar calculations can be applied to a helicopter blade based on its size and rotation rate.
Step-by-step explanation:
Calculating Centripetal Acceleration and Linear Speed of a Grinding Wheel
The question asks about calculating the centripetal acceleration and linear speed for a grindstone and a helicopter blade. Let's tackle the grindstone scenario first:
a) To calculate the centripetal acceleration of the grindstone at its edge, we use the formula a_c = r\(\omega^2\), where a_c is the centripetal acceleration, r is the radius, and \omega is the angular velocity. First, we must convert the angular velocity from revolutions per minute (rev/min) to radians per second (rad/s) by using the conversion factor that 1 rev/min is equivalent to \(\frac{2\pi}{60}\) rad/s.
- Angular velocity \(\omega = 6500 \times \frac{2\pi}{60}\) rad/s
- Radius r = 7.50\text{ cm} = 0.075\text{ m}
After calculation, the centripetal acceleration will then be expressed in meters per second squared (m/s^2), and we can further convert it into multiples of the standard acceleration due to gravity g (9.81 m/s^2).
b) The linear speed v of a point on the edge of the grinding wheel is determined using the relationship v = r\omega. Again, using the values we have for radius and angular velocity, we can find out the linear speed in meters per second (m/s).
When dealing with safety checks for abrasive grinding wheels, it's critical to ensure that the wheel is free of cracks or other damages, as these could lead to wheel failure under the stress of operation. Visual inspections, ring tests, and vibrations analysis are most commonly used to assess the integrity of grinding wheels.
For the helicopter blade, we would proceed with similar steps to those above but adapting the formulae to the given measurements of the helicopter blade's length and rotation speed to calculate the centripetal acceleration at the tip of the blade.