rotational equilibrium
... – If the net force on an object is zero, then the object is in translational equilibrium – If the net torque on an object is zero, then the object is in rotational equilibrium – THUS, for an object to be completely in equilibrium, the net force and the net torque must be zero – The dependence of equ ...
... – If the net force on an object is zero, then the object is in translational equilibrium – If the net torque on an object is zero, then the object is in rotational equilibrium – THUS, for an object to be completely in equilibrium, the net force and the net torque must be zero – The dependence of equ ...
Transforms - Lecture`s of computer graphics
... vectors, Cartesian vectors, vector magnitude, vector products, and area calculations. It also shows how vectors are used in lighting calculations and back-face detection. • Vectors provide us with some powerful techniques for computing angles between lines and the orientation of surfaces. They also ...
... vectors, Cartesian vectors, vector magnitude, vector products, and area calculations. It also shows how vectors are used in lighting calculations and back-face detection. • Vectors provide us with some powerful techniques for computing angles between lines and the orientation of surfaces. They also ...
Deformation Rotational Motion Rotation of Rigid Objects
... for the disc, a fixed reference Rotation of Rigid Objects line is chosen. A particle at P is located at a distance r from To begin, consider a rotating disc. the rotation axis through O. ...
... for the disc, a fixed reference Rotation of Rigid Objects line is chosen. A particle at P is located at a distance r from To begin, consider a rotating disc. the rotation axis through O. ...
15. Parallel Axis Theorem and Torque A) Overview B) Parallel Axis
... convention in order to match the usual measurement of the angle theta relative to the xaxis in a right-handed Cartesian coordinate system. There is a simple rule involving the right hand that can be used to define the directions of the angular velocity vector. Namely, if you curl the fingers of your ...
... convention in order to match the usual measurement of the angle theta relative to the xaxis in a right-handed Cartesian coordinate system. There is a simple rule involving the right hand that can be used to define the directions of the angular velocity vector. Namely, if you curl the fingers of your ...
Using Matlab to Calculate Top Performance
... • The moment of inertia of an object can change if its shape changes. Figure skaters who begin a spin with arms outstretched provide a striking example. By pulling in their arms, they reduce their moment of inertia, causing them to spin faster (by the conservation of angular momentum). ...
... • The moment of inertia of an object can change if its shape changes. Figure skaters who begin a spin with arms outstretched provide a striking example. By pulling in their arms, they reduce their moment of inertia, causing them to spin faster (by the conservation of angular momentum). ...
Rotation: Moment of Inertia and Torque
... that is free to rotate in all planes, as shown in Fig. 10, then the wheel will fall and oscillate like a pendulum. However, if the wheel is spinning sufficiently fast, it will rotate in a horizontal plane and will not swing like a pendulum. This motion is called precession. In Fig. 10, the red line ...
... that is free to rotate in all planes, as shown in Fig. 10, then the wheel will fall and oscillate like a pendulum. However, if the wheel is spinning sufficiently fast, it will rotate in a horizontal plane and will not swing like a pendulum. This motion is called precession. In Fig. 10, the red line ...
Slide 1
... certain instant its center of mass has a speed of 10.0 m/s. Determine (a) the translational kinetic energy of its center of mass, (b) the rotational kinetic energy about its center of mass, and (c) its total energy. ...
... certain instant its center of mass has a speed of 10.0 m/s. Determine (a) the translational kinetic energy of its center of mass, (b) the rotational kinetic energy about its center of mass, and (c) its total energy. ...
Lecture Notes
... The Rotational Variables In this chapter we will study the rotational motion of rigid bodies about fixed axes. A rigid body is defined as one that can rotate with all its parts locked together and without any change of its shape. A fixed axis means that the object rotates about an axis that does no ...
... The Rotational Variables In this chapter we will study the rotational motion of rigid bodies about fixed axes. A rigid body is defined as one that can rotate with all its parts locked together and without any change of its shape. A fixed axis means that the object rotates about an axis that does no ...
Lecture 8: Forces & The Laws of Motion
... 1) If an object is rotating at a constant angular speed which statement is true? a) the system is in equilibrium b) the net force on the object is ZERO c) the net torque on the object is ZERO d) all of the above ...
... 1) If an object is rotating at a constant angular speed which statement is true? a) the system is in equilibrium b) the net force on the object is ZERO c) the net torque on the object is ZERO d) all of the above ...
Lecture Mechanics Rigid Body ppt
... (ii) rotate upon its center To describe motion as a whole, need (i) x (t) (x = position of center for example), and (ii) angles q (t) and f (t), describing the angular orientation of the dumbbell with respect to a chosen coordinate system (rotation). ...
... (ii) rotate upon its center To describe motion as a whole, need (i) x (t) (x = position of center for example), and (ii) angles q (t) and f (t), describing the angular orientation of the dumbbell with respect to a chosen coordinate system (rotation). ...
Geometry: Unit 1: Transformations
... Transformations: Image and PreImage A transformation is a one-to-one correspondence between the points of the pre-image and the points of the image. A transformation guarantees that if our pre-image has three points, then our image will also have three points. Pre-Image: The figure prior to transfo ...
... Transformations: Image and PreImage A transformation is a one-to-one correspondence between the points of the pre-image and the points of the image. A transformation guarantees that if our pre-image has three points, then our image will also have three points. Pre-Image: The figure prior to transfo ...
Rotation
... Angular acceleration is directly proportional to the net torque, but the constant of proportionality has to do with both the mass of the object and the distance of the object from the axis of rotation – in this case the constant is mr2 ...
... Angular acceleration is directly proportional to the net torque, but the constant of proportionality has to do with both the mass of the object and the distance of the object from the axis of rotation – in this case the constant is mr2 ...
Rotation
... Angular acceleration is directly proportional to the net torque, but the constant of proportionality has to do with both the mass of the object and the distance of the object from the axis of rotation – in this case the constant is mr2 ...
... Angular acceleration is directly proportional to the net torque, but the constant of proportionality has to do with both the mass of the object and the distance of the object from the axis of rotation – in this case the constant is mr2 ...
F - Cloudfront.net
... vector r. To determine the angle between the direction of r and the direction of each force, we shift the force vectors of Fig.a, each in turn, so that their tails are at the origin. Figures b, c, and d, which are direct views of the xz plane, show the shifted force vectors F1, F2, and F3. respect ...
... vector r. To determine the angle between the direction of r and the direction of each force, we shift the force vectors of Fig.a, each in turn, so that their tails are at the origin. Figures b, c, and d, which are direct views of the xz plane, show the shifted force vectors F1, F2, and F3. respect ...
Angular Momentum - Piri Reis Üniversitesi
... A disk rotating around its centre I = mr2/2 (if it rotates about the y axis it is I = mr2/4) A sphere rotating around any axis through the centre, I = 2mr2/5 A uniform road of length L rotating around its centre I = mL2/12 A simple point mass around an axis is the same as a hollow cylinder I ...
... A disk rotating around its centre I = mr2/2 (if it rotates about the y axis it is I = mr2/4) A sphere rotating around any axis through the centre, I = 2mr2/5 A uniform road of length L rotating around its centre I = mL2/12 A simple point mass around an axis is the same as a hollow cylinder I ...
Virtual 3D Manipulation Using Cutting Plane Lines
... arbitrary trajectory can be achieved by alternately executing the last two phases. The phase switches by releasing and pressing the left button within about 200 msec. Figure 6 shows simplified state transitions among three phases and the normal phase (Neutral). In the figure, “Press” stands for the ...
... arbitrary trajectory can be achieved by alternately executing the last two phases. The phase switches by releasing and pressing the left button within about 200 msec. Figure 6 shows simplified state transitions among three phases and the normal phase (Neutral). In the figure, “Press” stands for the ...
Craniovertebral Joints
... – Two lateral zygapophysial joints between the articular surfaces of the inferior articular processes of the atlas, and the superior processes of the axis – Two medial joints: one between the anterior surface of the dens of the axis, and the anterior surface of the atlas, and the other between the p ...
... – Two lateral zygapophysial joints between the articular surfaces of the inferior articular processes of the atlas, and the superior processes of the axis – Two medial joints: one between the anterior surface of the dens of the axis, and the anterior surface of the atlas, and the other between the p ...
RotationalMotion - University of Colorado Boulder
... Angle of a rigid object is measured relative to some reference orientation, just like 1D position x is measured relative to some reference position (the origin). Angle is the "rotational position". Like position x in 1D, rotational position has a sign convention. Positive angles are CCW (count ...
... Angle of a rigid object is measured relative to some reference orientation, just like 1D position x is measured relative to some reference position (the origin). Angle is the "rotational position". Like position x in 1D, rotational position has a sign convention. Positive angles are CCW (count ...
t - cs.csustan.edu - California State University Stanislaus
... • Geometrically, a point is a position in space • Algebraically, the point is defined by its coordinates (x,y) or (x,y,z) • We will usually see points as vertices in a geometric object • However, a triple (x,y,z) or a quadruple (x,y,z,w) will sometimes have another meaning, such as a color ...
... • Geometrically, a point is a position in space • Algebraically, the point is defined by its coordinates (x,y) or (x,y,z) • We will usually see points as vertices in a geometric object • However, a triple (x,y,z) or a quadruple (x,y,z,w) will sometimes have another meaning, such as a color ...
Rotational Motion - University of Colorado Boulder
... Angle of a rigid object is measured relative to some reference orientation, just like 1D position x is measured relative to some reference position (the origin). Angle is the "rotational position". Like position x in 1D, rotational position has a sign convention. Positive angles are CCW (count ...
... Angle of a rigid object is measured relative to some reference orientation, just like 1D position x is measured relative to some reference position (the origin). Angle is the "rotational position". Like position x in 1D, rotational position has a sign convention. Positive angles are CCW (count ...
10-2 - Learning
... For translational motion, Newton's second law connects the force acting on a particle with the resulting acceleration. There is a similar relationship between the torque of a force applied on a rigid object and the resulting angular acceleration. This equation is known as Newton's second law for rot ...
... For translational motion, Newton's second law connects the force acting on a particle with the resulting acceleration. There is a similar relationship between the torque of a force applied on a rigid object and the resulting angular acceleration. This equation is known as Newton's second law for rot ...
Torque and Rotational Inertia Torque
... The drawing shows an A-shaped ladder. Both sides of the ladder are equal in length. This ladder is standing on a frictionless horizontal surface, and only the crossbar (which has a negligible mass) of the "A" keeps the ladder from collapsing. The ladder is uniform and has a mass of 14.0 kg. Determin ...
... The drawing shows an A-shaped ladder. Both sides of the ladder are equal in length. This ladder is standing on a frictionless horizontal surface, and only the crossbar (which has a negligible mass) of the "A" keeps the ladder from collapsing. The ladder is uniform and has a mass of 14.0 kg. Determin ...
Quaternions and spatial rotation
Unit quaternions, also known as versors, provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions. Compared to Euler angles they are simpler to compose and avoid the problem of gimbal lock. Compared to rotation matrices they are more numerically stable and may be more efficient. Quaternions have found their way into applications in computer graphics, computer vision, robotics, navigation, molecular dynamics, flight dynamics, orbital mechanics of satellites and crystallographic texture analysis.When used to represent rotation, unit quaternions are also called rotation quaternions. When used to represent an orientation (rotation relative to a reference coordinate system), they are called orientation quaternions or attitude quaternions.