Final answer:
The linear speed of a point on the edge of a 7.50 cm radius workshop grindstone rotating at 6500 rev/min is approximately 51.13 m/s. This speed is calculated using the formula v = r * ω and converting the rotational speed from rev/min to rad/s.
Step-by-step explanation:
Calculating the Linear Speed of a Point on the Grindstone's Edge
The question involves finding the linear (or tangential) speed of a point on the edge of a workshop grindstone that has a radius and rotates at a known speed. First, we'll convert the rotational speed from revolutions per minute (rev/min) to radians per second (rad/s), and then use this to find the linear speed.
Given:
- Radius (r): 7.50 cm (or 0.075 m)
- Rotational speed: 6500 rev/min
Using the formula for linear speed v = r * ω, where ω is the angular speed, we can calculate v as follows:
- Convert rev/min to rad/s: ω = 6500 rev/min * (2π rad/rev) * (1 min/60 s)
- ω ≈ 681.77 rad/s
- Linear speed v = 0.075 m * 681.77 rad/s
- v ≈ 51.13 m/s
Therefore, the linear speed of a point on the edge of the grindstone is approximately 51.13 m/s.