Auniform solid sphere of mass m and radius r rotates with an angular speed ω about an axis through its center. a uniform solid cylinder of mass m, radius r, and length 2r rotates through an axis running through the central axis of the cylinder. what must be the angular speed of the cylinder so it will have the same rotational kinetic energy as the sphere?

Explanation:

Rotational inertia of uniform solid sphere is given as

now we have its angular speed given as

angular speed =

now we have its final rotational kinetic energy as

now the rotational inertia of solid cylinder about its axis is given by

now let say its angular speed is given as

angular speed =

now its rotational kinetic energy is given by

now if rotational kinetic energy of solid sphere is same as rotational kinetic energy of solid sphere then

a charge 3q is at the origin, and a charge −2q is on the positive x axis at x=a. part a where on the x-axis would you place a third charge so it would experience no net electric force? enter an expression for the exact answer, which will involve a square-root sign. (do not enter an approximate decimal answer.)

  distance on the y-axis and time on the x-axis.

explanation:

the instantaneous velocity = change in position/time taken

the slope of the graph should give instantaneous velocity.

  slope of a graph = change in value of y -axis / change in values of x -axis

  comparing both the equations

    change in value of y -axis = change in position

  change in values of x -axis = time taken

so position values should be on the y axis and time values should be on the x axis.

distance on the y-axis and time on the x-axis.