F2 F2=150 N 12=1 m F1 F3=200 N r3-0.5 m F3 The following uniform rod has a moment of inertia = 10 kgm? a) Calculate the net torque. b) Calculate the angular acceleration of the rod. c) If the rod starts from rest, calculate its angular velocity 5 seconds later (in rpm).

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**Torque, Angular Acceleration, and Angular Velocity of a Uniform Rod**

*Problem Statement:*

A uniform rod has a moment of inertia \( I = 10 \, \text{kgm}^2 \). The rod experiences three forces (F1, F2, and F3) at different points along its length, each exerting torque about the center of mass. The forces act perpendicularly to the rod in the following manner:

- \( F1 = 100 \, \text{N} \) at a distance \( r1 = 1 \, \text{m} \) from the center.
- \( F2 = 150 \, \text{N} \) at a distance \( r2 = 1 \, \text{m} \) from the center.
- \( F3 = 200 \, \text{N} \) at a distance \( r3 = 0.5 \, \text{m} \) from the center.

*Tasks:*

a) Calculate the net torque acting on the rod.
b) Determine the angular acceleration of the rod.
c) If the rod starts from rest, find its angular velocity after 5 seconds (expressed in revolutions per minute, rpm).

*Diagram Explanation:*

The diagram displays a horizontal rod with three forces applied perpendicularly:
- \( F1 \) acts downward on the left side.
- \( F2 \) acts downward on the right side.
- \( F3 \) acts upward at the center-bottom of the rod.

These forces create torque around the center of mass indicated by a dot in the middle of the rod.

The problem requires applying principles of rotational dynamics to solve for net torque, angular acceleration, and eventual angular velocity.
Transcribed Image Text:**Torque, Angular Acceleration, and Angular Velocity of a Uniform Rod** *Problem Statement:* A uniform rod has a moment of inertia \( I = 10 \, \text{kgm}^2 \). The rod experiences three forces (F1, F2, and F3) at different points along its length, each exerting torque about the center of mass. The forces act perpendicularly to the rod in the following manner: - \( F1 = 100 \, \text{N} \) at a distance \( r1 = 1 \, \text{m} \) from the center. - \( F2 = 150 \, \text{N} \) at a distance \( r2 = 1 \, \text{m} \) from the center. - \( F3 = 200 \, \text{N} \) at a distance \( r3 = 0.5 \, \text{m} \) from the center. *Tasks:* a) Calculate the net torque acting on the rod. b) Determine the angular acceleration of the rod. c) If the rod starts from rest, find its angular velocity after 5 seconds (expressed in revolutions per minute, rpm). *Diagram Explanation:* The diagram displays a horizontal rod with three forces applied perpendicularly: - \( F1 \) acts downward on the left side. - \( F2 \) acts downward on the right side. - \( F3 \) acts upward at the center-bottom of the rod. These forces create torque around the center of mass indicated by a dot in the middle of the rod. The problem requires applying principles of rotational dynamics to solve for net torque, angular acceleration, and eventual angular velocity.
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