Planar Kinematics of a Rigid Body

In summary, the truck is moving to the right with a speed of 12km/h (3.3333m/s) while a pipe section in its bed with a radius of 1.25m and center at C is moving without slipping at a relative velocity of 2m/s to the truck. The angular velocity of the pipe section is 1.6 rad/s and the absolute velocity of C is 5.3333m/s to the right. The formula Vc = Vo + Vc/o was used to calculate the absolute velocity of C.
  • #1
Gnat85
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0

Homework Statement



A truck is moving to the right with a speed of Vo=12km/h=3.3333m/s while the pipe section in its bed has a radius R=1.25m and a center at C that rolls without slipping over the truck's bed. The center of the pipe section C is moving to the right at 2m/s relative to the truck. Determine the angular velocity of the pipe section and the absolute velocity of C.

Homework Equations


Vc = Vo +Vc/o

The Attempt at a Solution


Vc = 3.3333+2 = 5.3333m/s
5.3333=3.3333+1.25w (w is omega) w=1.6 rad/s (this is my angular velocity) I am confused in how to find the absolute velocity...can anyone help?
 
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  • #2




Thank you for your question. Based on the information provided, the absolute velocity of C can be found using the formula Vc = Vo + Vc/o, where Vc is the absolute velocity of C, Vo is the velocity of the truck, and Vc/o is the relative velocity of C with respect to the truck. Plugging in the values given, we get Vc = 3.3333 + 2 = 5.3333m/s. Therefore, the absolute velocity of C is 5.3333m/s to the right. I hope this helps. Let me know if you have any further questions.
Scientist
 

1. What is planar kinematics of a rigid body?

Planar kinematics of a rigid body is a branch of mechanics that studies the motion of a solid object in a two-dimensional plane. It involves analyzing the positions, velocities, and accelerations of different points on the rigid body as it moves through space.

2. What is the difference between planar kinematics and planar dynamics?

The main difference between planar kinematics and planar dynamics is that kinematics deals with the motion of a rigid body without considering the forces that cause the motion, while dynamics focuses on the forces and torques that cause the motion of the body.

3. What are the main types of motion in planar kinematics?

The main types of motion in planar kinematics are translation, rotation, and general motion. Translation is when all points on the body move in parallel and maintain the same orientation. Rotation is when the body moves about a fixed point, and general motion is a combination of translation and rotation.

4. How is the motion of a rigid body described in planar kinematics?

The motion of a rigid body in planar kinematics is described using position, velocity, and acceleration vectors. These vectors represent the displacement, change in displacement, and change in velocity of different points on the rigid body, respectively.

5. What are some real-world applications of planar kinematics of a rigid body?

Planar kinematics of a rigid body has many real-world applications, including the design and analysis of machines, vehicles, and structures. It is also used in robotics, biomechanics, and animation to simulate and control the motion of objects in a two-dimensional plane.

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