PHYSICS 181 Lecture Notes - Lecture 3: Dot Product, Cross Product, Unit Vector

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cerisebuffalo390

28 Sep 2016

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Phys181 lecture 3 vector operations ii. If false, give an example where it fails: a. The magnitude of ab is a b: b. A. fails when a and b are not antiparallel, b. fails when the magnitude is not parallel, d. fails when b or a are negative, e. fails in cases where there is no right angles. Unit vectors are i, j, and k with a little ^ over them: unit vectors are always equal to 1, these represent vectors lying on the x, y, and z axis. These vectors purpose is to indicate the vector is on the axis. The x-axis is represented by: i = (1, 0, 0) The y-axis is represented by: j = (0, 1, 0) The z-axis is represented by: k = (0, 0, 1) Remember that the unit vectors are equal to 1, and are only there to represent the direction (they are not variables)

Related Questions

The displacement vector Ã has scalar components of Ax = 80.0 m and Ay = 60.0 m. The displacement vector B has a scalar component of Bx = 60.0 m, and the magnitude of B = 75.0 m. The displacement C has a magnitude of C = 100.00 m and is directed at an angle of 36.9 degrees above the positive x-axis. Two of these vectors are equal. Determine which two and support your choice with a calculation.

emeraldgerbil245

(A) Show that the position of a particle on a circle of radius Rwith center at the origin (x=0,y=0) is given in unit vectors byr=cosÎ¸i+sinÎ¸j, where Î¸ is the angle of the position vector with thex axis.

B) If the particle moves with constant speed v and period T,starting on the x axis at t=0, find an expression for Î¸ in terms ofthe time and T.

C) Differentiate the position vector twice with respect to timeto find the acceleration and show that it is the centripetalacceleration, whose magnitude is given by equation (a=(v^2)/r) andwhose direction is toward the center of the circle. (Not that theunit vectors i and j are constants, independent of time.)

Object A collides on a horizontal frictionless surface with an initially stationary target, object X. The initial and final velocities of object A are shown. The final velocity of object X is not given.

a). At an instant during the collision, is the net force on object A zero or non-zero?

b) [During the collision, is the momentum of object A conserved? Explain. Is the momentum of the system consisting of objects A and X conserved? Explain. On the same horizontal surface, object C collides with an initially stationary target, object Z. The initial speeds of objects C and A are the same, and m_x = m_z > m_A = m_c. After the collisions, object C moves in the direction shown and has the same final speed as object A. In the space below, copy the vectors v_C1 and v_cr with their tails together. Use these vectors to draw the change in velocity vector for glider C, Delta v_c. Is the magnitude of the change in velocity vector of object A greater than, less than, or equal to the magnitude of the change in velocity vector of object C? Explain? Is the magnitude of the change in the momentum vector of object A greater than, less than, or equal to the magnitude of the change in the momentum vector of object C? Explain? Is the final speed of object X greater than, less than, or equal to the final speed of object Z? Explain. Consider the following incorrect statement: Gliders A and C have some change in momentum. They have the same mass, and because they have the same initial speed and same final speed. Delta-v is the same for each of.them." Discuss the error(s) in the reasoning.

sangriaporcupine175

PHYSICS 181 Lecture Notes - Lecture 3: Dot Product, Cross Product, Unit Vector

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