It is desired that the outer edge of a grinding wheel 9.0 cm in radius move at a rate of 6.0 m/s.

The angular speed is___rad/s.
A thread of length m could be wound on the rim of the wheel in 3.0 s when it is turning at this rate?
Nearest whole number.

Electric charge is uniformly distributed inside a nonconducting sphere of radius 0.30 m. the electric field at a point p, which is 0.50 m from the center of the sphere, is 15,000 n/c and is directed radially outward. what is the maximum magnitude of the electric field due to this sphere

Avoltage source vs = 10 v is in series with a resistor of 10 kohm. if the source transformation theorem is applied, what will the value of the current source be in ma ?

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.