A person holds a ladder horizontally at its center. Treating the ladder as a uniform rod of length 3.55 m and mass 10.31 Kg, find the torque the person must exert on the ladder to give it an angular acceleration of 0.406 rad/s2.
Should I set the given angular acceleration equal to Torque/ (1/3 * m* r2) and solve for Torque?
Yes.
Yes, you are on the right track. To determine the torque the person must exert on the ladder, you can use the equation:
Torque = (1/3) * m * r^2 * angular acceleration
Given:
Length of the ladder (L) = 3.55 m
Mass of the ladder (m) = 10.31 kg
Angular acceleration (α) = 0.406 rad/s^2
First, calculate the radius of the ladder (r) by dividing the length by 2, since the ladder is held horizontally at its center:
r = L/2 = 3.55/2 = 1.775 m
Now, substitute the known values into the equation and solve for torque:
Torque = (1/3) * 10.31 * (1.775)^2 * 0.406
Calculating this gives you the value of torque in Newton-meters (Nm).