2. Two rigid links are rotating in the horizontal plane as shown in the figure below. The left-most link rotates with an angular rate \(\dot{\theta}_1\) of 4 rad/s. The end of the right-most link holds a pin which is confined to move along a slot in the other link. The length of the right-most link \(r_2\) is 0.45 m. Determine the angular rate \(\dot{\theta}_2\) of the second link at the instant shown. Use \(\theta_1 = 30^\circ\), \(\theta_2 = 60^\circ\), and \(r_1 = 0.6\) m.### Diagram Explanation:A diagram is shown with two rigid links connected. The left-most link rotates with an angular motion denoted by the angle \(\theta_1\) and has an angular velocity \(\dot{\theta}_1\). The second link, which is the right-most one, is pinned and able to move along a slot on the first link, marked by an angle \(\theta_2\). The physical lengths of these links are labeled as \(r_1\) and \(r_2\). The angles and lengths form a geometric and kinematic arrangement that needs solving to find the angular rate \(\dot{\theta}_2\) of the second link. The angle \(\theta_1\) within the arrangement is set at \(30^\circ\), while \(\theta_2\) is set at \(60^\circ\), with each link having specified lengths of \(r_1 = 0.6\) m and \(r_2 = 0.45\) m.

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Description: 2. Two rigid links are rotating in the horizontal plane as shown in the figure below. The left-most link rotates with an angular rate \(\dot{\theta}_1\) of 4 rad/s. The end of the right-most link holds a pin which is confined to move along a slot in

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2. Two rigid links are rotating in the horizontal plane as shown in the figure below. The left-most link rotates with angular rate ₁ of 4 rad/s. The end of the right-most link holds a pin which is confined to move along a slot in the other link. The length of the right-most link 12 is 0.45 m. Determine the angular rate ₂ of the second link at the instant shown. Use 0₁ = 30°, 0₂ = 60°, and r₁=0.6 m.

2. Two rigid links are rotating in the horizontal plane as shown in the figure below. The left-most link rotates with angular rate ₁ of 4 rad/s. The end of the right-most link holds a pin which is confined to move along a slot in the other link. The length of the right-most link 12 is 0.45 m. Determine the angular rate ₂ of the second link at the instant shown. Use 0₁ = 30°, 0₂ = 60°, and r₁=0.6 m.

Elements Of Electromagnetics

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ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Concept explainers

Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

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Question

2. Two rigid links are rotating in the horizontal plane as shown in the figure below. The left-most link rotates with an angular rate \(\dot{\theta}_1\) of 4 rad/s. The end of the right-most link holds a pin which is confined to move along a slot in the other link. The length of the right-most link \(r_2\) is 0.45 m. Determine the angular rate \(\dot{\theta}_2\) of the second link at the instant shown. Use \(\theta_1 = 30^\circ\), \(\theta_2 = 60^\circ\), and \(r_1 = 0.6\) m.

### Diagram Explanation:

A diagram is shown with two rigid links connected. The left-most link rotates with an angular motion denoted by the angle \(\theta_1\) and has an angular velocity \(\dot{\theta}_1\). The second link, which is the right-most one, is pinned and able to move along a slot on the first link, marked by an angle \(\theta_2\). The physical lengths of these links are labeled as \(r_1\) and \(r_2\). The angles and lengths form a geometric and kinematic arrangement that needs solving to find the angular rate \(\dot{\theta}_2\) of the second link. The angle \(\theta_1\) within the arrangement is set at \(30^\circ\), while \(\theta_2\) is set at \(60^\circ\), with each link having specified lengths of \(r_1 = 0.6\) m and \(r_2 = 0.45\) m.

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