How Is Maximum Torque Calculated from RPM and Force?

[raju.prithiv]

Homework Statement

Find the maximum torque
given:
500RPM
30N

Please the Attached picture for detailed information

Homework Equations

The Attempt at a Solution

 

[mark726]

To find the maximum torque, we will use the formula T = F x r, where T is torque, F is force, and r is the distance from the axis of rotation to the point where the force is applied. In this case, we are given the force of 30N, but we need to determine the distance r.

To do this, we can use the formula for linear velocity, v = ωr, where v is linear velocity, ω is angular velocity, and r is the distance from the axis of rotation. We are given the angular velocity of 500RPM, which can be converted to radians per second by multiplying by 2π/60. This gives us an angular velocity of 52.36 radians per second.

Now, we can rearrange the formula to solve for r:

r = v/ω

Plugging in the values we have, we get:

r = (30N)/(52.36 rad/s)
r = 0.573 meters

Now that we have the distance r, we can plug it into our original formula for torque:

T = (30N)(0.573m)
T = 17.19 Nm

Therefore, the maximum torque in this scenario is 17.19 Nm.