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Problem: 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 F1 = 1.5 N, F2 = 3.5 N, F3 = 11 N, and F4 = 15.5 N, F2 acts as a distance d = 0.28 m from the center of mass.Part A. Calculate the magnitude τ1 of the torque due to force F1 in N•m.Part B. Calculate the magnitude τ2 of the torque due to force F2 in N•m.Part C. Calculate the magnitude τ3 of the torque due to force F3 in N•m.Part D. Calculate the magnitude τ4 of the torque due to force F4 in N•m.Part E. Calculate the angular acceleration a of the thin rod about its center of mass in rad/s2. Let the counter-clockwise direction be positive.

FREE Expert Solution

Torque:

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

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°

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Problem Details

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 F1 = 1.5 N, F2 = 3.5 N, F3 = 11 N, and F4 = 15.5 N, F2 acts as a distance d = 0.28 m from the center of mass.

Part A. Calculate the magnitude τ1 of the torque due to force F1 in N•m.

Part B. Calculate the magnitude τ2 of the torque due to force F2 in N•m.

Part C. Calculate the magnitude τ3 of the torque due to force F3 in N•m.

Part D. Calculate the magnitude τ4 of the torque due to force F4 in N•m.

Part E. Calculate the angular acceleration a of the thin rod about its center of mass in rad/s2. Let the counter-clockwise direction be positive.

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.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Bompadre's class at MIZZOU.