Classical mechanics - rotating systems
Set your coordinate system with the origin in the middle of the platform at the axis of
rotation) with the x-axis oriented so that at t=0, the puck is located along the x-axis.
Ignore the rotation of the earth
A student is on the edge of a frictionless platform of diameter 60/ meters which is
rotating at I revolution per minute (1) in a counterclockwise direction. They wish to send
a puck across the platform so that they can catch it after they have rotated half a turn.
Assuming the puck leaves and is caught exactly at the edge of the platform
a. Determine the required initial velocity as seen by an inertial observer standing
beside the platform.
b. Determine the required initial velocity as seen by the student rotating on the
platform (use your solution to part a. for this.
c. Determine the equations of motion for the puck in the rotating coordinate
system (1.e. the equations that would describe the trajectory of the puck as seen
by the student)
d. Solve these equations by defining a new complex function, mu (t)=x(t)+iy(t), and
the solution is
eta (t)=e^(-iOmega t)(C_(1)+C_(2)t)
where C1 and C2 are constants (possibly complex)
which are chosen to satisfy the initial conditions. Determine these constants and check
to confirm that the puck will arrive at the expected location after half a rotation.
Classical mechanics - rotating systems
Set your coordinate system with the origin in the middle of the platform at the axis of rotation) with the X-axis oriented so that at t =0, the puck is located along the X-axis. Ignore the rotation of the earth
A student is on the edge of a frictionless platform of diameter 60/ meters which is rotating at I revolution per minute (1) in a counterclockwise direction. They wish to send a puck across the platform so that they can catch it after they have rotated half a turn. Assuming the puck leaves and is caught exactly at the edge of the platform
a. Determine the required initial velocity as seen by an inertial observer standing beside the platform. b. Determine the reguired initial velocity as seen by the student rotating on the platform (use your solution to part a. for this. c. Determine the equations of motion for the puck in the rotating coordinate system (l.e. the equations that would describe the traiectory of the puck as seen by the student) d. Solve these equations by defining a new complex function, (t) = x(t) +i y(t), and the solution is =e-ii(C+Ct * where C1 and c2 are constants (possibly complex) which are chosen to satisfy the initial conditions. Determine these constants and check to confirm that the puck will arrive at the expected location after half a rotation.
