(a) To calculate the angular velocity, we need to convert the rotation rate from revolutions per minute to radians per second.
1 rpm = (2 * π) rad/min.
Therefore, 2400 rpm = 2400 * (2 * π) rad/min = 4800 * π rad/min.
Now we need to convert this to rad/s:
1 min = 60 s.
So, 4800 * π rad/min = (4800 * π) / 60 rad/s = 80 * π rad/s.
The angular velocity is 80π rad/s.
(b) The linear speed (v) of a point on the edge of the grinding wheel can be calculated using the formula:
v = r * ω,
where r is the radius of the grinding wheel, and ω is the angular velocity.
The radius of the grinding wheel is half its diameter, which is 0.62 m / 2 = 0.31 m.
So, the linear speed is:
v = 0.31 m * 80π rad/s ≈ 77.92 m/s.
The radial (centripetal) acceleration (a) can be calculated using the formula:
a = r * ω^2.
So, the radial acceleration is:
a = 0.31 m * (80π rad/s)^2 ≈ 193867.6 m/s².
Thus, the linear speed is approximately 77.92 m/s, and the radial acceleration is approximately 193867.6 m/s².
A grinding wheel 0.62 m in diameter rotates at 2400 rpm.
(a) Calculate its angular velocity in rad/s.
rad/s
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel?
linear speed m/s
radial acceleration m/s2
1 answer
1 answer