If you know two vectors’ components, A → = ( A x , A y , A z ) ,  and  B → = ( B x , B y , B z ) , {“version”:”1.1″,”math”:”\vec{A}=(A_x,A_y,A_z), \mbox{ and } \vec{B}=(B_x,B_y,B_z), “}how can you determine whether these vectors are perpendicular to each other?

Please draw the standard xy coordinate system on a paper sheet. This paper sheet lies on a table. A little alien visits from outer space, takes out a little bicycle, and rides on the sheet along the x-axis in its positive direction at constant velocity. What is the direction of the angular momentum of a bicycle wheel?

Find the angle between vectors F = (3, 0, 4) and d = (1, -2, 2).

A body of mass 10 kg is initially at rest on a horizontal surface. The coefficient of static friction between the body and the surface is 0.7, and the coefficient of kinetic friction is 0.4. A horizontal force 50 N is applied to the body. What is the friction force acting on the body?

An object is displaced by r → = ( 5 m ) i ^ − ( 2 m ) j ^ {“version”:”1.1″,”math”:”\vec{r}=(5\,m)\hat{i}-(2\,m)\hat{j}”} while it is acted upon by  F → = − ( 8 N ) i ^ + ( 22 N ) j ^ . {“version”:”1.1″,”math”:”\vec{F}=-(8\, N)\hat{i}+(22\,N)\hat{j}.”}What is the work done on the object by this force?

One end of a string is tied to a wall, with a length L = 1.1 m from the wall to the point where the string touches a pulley. The other end passes over the frictionless pulley and is connected to a block of mass m = 0.35 kg. When the string is stretched over the pulley, its linear mass density is 4.40 × 10-4 kg/m. What is the wavelength of the third mode of standing wave on this string?

A solid disk is mounted so it can rotate without friction about an axis through its center. Initially, it rotates with some angular velocity ω0{“version”:”1.1″,”math”:”ω0″}. A second disk, initially not rotating, is dropped concentrically onto the disk. The second disk has the same mass and half the radius of the first disk. When the two come to a common rotation, what is the final angular velocity?

Compute the torque on a uniform rod of length L and mass M from the figure below if the positive z direction is out of the page.

Consider the Atwood machine in the figure below. If the pulley is massless and m1=3m2{“version”:”1.1″,”math”:”m1=3m2″}, what is the magnitude of the acceleration of the system?

A figure skater on a frictionless ice is rotating with her arms and a leg outstretched. She brings her arms and leg in, causing her rotational speed to increase. Which of the following quantities is conserved during her spin?