A uniform thin rod of mass m = 2.9kg and length L = 1.3 m can rotate about an axle through its centerFour forces are acting on it as shown in the figure. Their magnitudes are F_{1} =; 8.5N, F_{2} = 3.5N; F_{3} = 13.5N and F 4 =19.5N.F 2 acts a distance d = 0.16 m from the center of mass. Part (a) calculate the magnitude t1 of the torque due to for e f1, in newton meters Part b :calculate the magnitude t2 of rhe torque due to foce f2 in newton meters Part c calculate the magnitude t3 of the torque due to force f3 in newton meters Part d calculate the magnitude t4 of the torque due to force f4 in newton meters Part eCalculate the angular acceleration a of the thin rod about its center of mass in radians per square second
A uniform thin rod of mass m = 2.9kg and length L = 1.3 m can rotate about an axle through its centerFour forces are acting on it as shown in the figure. Their magnitudes are F_{1} =; 8.5N, F_{2} = 3.5N; F_{3} = 13.5N and F 4 =19.5N.F 2 acts a distance d = 0.16 m from the center of mass. Part (a) calculate the magnitude t1 of the torque due to for e f1, in newton meters Part b :calculate the magnitude t2 of rhe torque due to foce f2 in newton meters Part c calculate the magnitude t3 of the torque due to force f3 in newton meters Part d calculate the magnitude t4 of the torque due to force f4 in newton meters Part eCalculate the angular acceleration a of the thin rod about its center of mass in radians per square second
A uniform thin rod of mass m = 2.9kg and length L = 1.3 m can rotate about an axle through its centerFour forces are acting on it as shown in the figure. Their magnitudes are F_{1} =; 8.5N, F_{2} = 3.5N; F_{3} = 13.5N and F 4 =19.5N.F 2 acts a distance d = 0.16 m from the center of mass. Part (a) calculate the magnitude t1 of the torque due to for e f1, in newton meters Part b :calculate the magnitude t2 of rhe torque due to foce f2 in newton meters Part c calculate the magnitude t3 of the torque due to force f3 in newton meters Part d calculate the magnitude t4 of the torque due to force f4 in newton meters Part eCalculate the angular acceleration a of the thin rod about its center of mass in radians per square second
A uniform thin rod of mass m = 2.9kg and length L = 1.3 m can rotate about an axle through its centerFour forces are acting on it as shown in the figure. Their magnitudes are F_{1} =; 8.5N, F_{2} = 3.5N; F_{3} = 13.5N and F 4 =19.5N.F 2 acts a distance d = 0.16 m from the center of mass.
Part (a) calculate the magnitude t1 of the torque due to for e f1, in newton meters
Part b :calculate the magnitude t2 of rhe torque due to foce f2 in newton meters
Part c calculate the magnitude t3 of the torque due to force f3 in newton meters
Part d calculate the magnitude t4 of the torque due to force f4 in newton meters
Part eCalculate the angular acceleration a of the thin rod about its center of mass in radians per square second Let the counter-clockwise direction be positive
Transcribed Image Text:**Learning about Forces and Moments**
In this diagram, we depict various forces acting on a rigid body, providing insight into the concepts of forces and moments crucial in physics and engineering.
### Diagram Description:
- **F1**: A horizontal force acting to the right.
- **F2**: A force acting at a 45° angle upwards to the left.
- **F3**: A force acting at a 60° angle downwards to the left.
- **F4**: A vertical force acting downwards.
The distances to the point where these forces act from a reference line are important to note:
- The line labeled "d" represents the perpendicular distance from the reference point to the line of action of force **F1**.
The diagram helps us understand how multiple forces applied at different angles impact the rigid body and how we calculate the resultant force and the resulting moments about a particular point.
### Key Concepts:
1. **Resultant Force**: The overall force acting on the body can be determined by vector addition of all the individual forces.
2. **Moment of a Force**: Also known as torque, is calculated as the product of the force and the perpendicular distance to the pivot point (in this case, distance "d"). Moments can cause rotational motion.
3. **Equilibrium**: For the body to be in equilibrium, the sum of all forces and the sum of all moments around any point must be zero.
Understanding this diagram is essential for solving problems related to statics where balancing forces and moments ensure structural stability and integrity.
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
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