A grinding wheel 0.40 m in diameter rotates at 2200 rpm.
What is the acceleration of a point on the edge of the grinding wheel?
To determine the acceleration of a point on the edge of the grinding wheel, we can use the formula for centripetal acceleration:
ac = (v^2) / r
Where:
ac is the centripetal acceleration,
v is the linear velocity, and
r is the radius of the circle.
1. First, we need to calculate the linear velocity (v).
To do this, we can use the formula:
v = ω * r
Where:
v is the linear velocity,
ω (omega) is the angular velocity, and
r is the radius of the circle.
2. We are given the angular velocity (ω) in rpm. To convert it to radians per second (rad/s), we need to multiply it by (2π/60) since there are 2π radians in a complete revolution and 60 seconds in a minute.
ω = (2200 rpm) * (2π rad/60 s)
3. Now we can calculate the linear velocity (v). We are given the diameter of the grinding wheel, but we need to convert it to the radius (r) by dividing it by 2.
r = (0.40 m) / 2 = 0.20 m
v = (ω) * (r)
4. Once we have the linear velocity (v), we can calculate the centripetal acceleration (ac).
ac = (v^2) / r
Plug in the values and calculate to get the answer.