Torque:

$\overline{){\mathbf{\tau}}{\mathbf{=}}{\mathbf{r}}{\mathbf{\xb7}}{\mathbf{F}}{\mathbf{s}}{\mathbf{i}}{\mathbf{n}}{\mathbf{\theta}}}$

Moment of inertia of a rod about its center of mass:

$\overline{){\mathbf{I}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{3}}{\mathbf{M}}{{\mathbf{L}}}^{{\mathbf{2}}}}$

Angular acceleration and torque are related by:

$\overline{){{\mathbf{\tau}}}_{\mathbf{n}\mathbf{e}\mathbf{t}}{\mathbf{=}}{\mathbf{I}}{\mathbf{\alpha}}}$

Where I is the moment of inertia.

**(A)**

F = 1.5 N

r = L/2 = 1.2/2 = 0.6 m

θ = 90°

A uniform thin rod of mass m = 2.6 kg and length L = 1.2 m can rotate about an axle through its center. Four forces are acting on it as shown in the figure. Their magnitudes are F_{1} = 1.5 N, F_{2} = 3.5 N, F_{3} = 11 N, and F_{4} = 15.5 N, F_{2} acts as a distance d = 0.28 m from the center of mass.

Part A. Calculate the magnitude τ_{1} of the torque due to force F_{1} in N•m.

Part B. Calculate the magnitude τ_{2} of the torque due to force F_{2} in N•m.

Part C. Calculate the magnitude τ_{3} of the torque due to force F_{3} in N•m.

Part D. Calculate the magnitude τ_{4} of the torque due to force F_{4} in N•m.

Part E. Calculate the angular acceleration a of the thin rod about its center of mass in rad/s^{2}. Let the counter-clockwise direction be positive.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Intro to Torque concept. You can view video lessons to learn Intro to Torque. Or if you need more Intro to Torque practice, you can also practice Intro to Torque practice problems.