- #1
doktorwho
- 181
- 6
Homework Statement
With the equations of motion in polar coordinates given by ##r(t)=pcos{kt^2}, φ(t)=kt^2## determine the velocity intensity of a point ##M## on the circumference of a cylinder which is rolling without friction on a horizontal plane at time ##t## is the velocity of the center of cylinder at time ##t## is ##v_c##
Homework Equations
3. The Attempt at a Solution [/B]
I first drew a picture of a cylinder and noted that the angle ##φ## is the angle from the horizontal to the point ##M## and i need to use another angle which is more suited for this rolling motion and that would be the angle ##\theta## which is measured from the radius to the vertical.
From here ##\theta=2φ=2kt^2##. Since i know how the angle changes, i can calculate the angular velocity and acceleration. ##ω=\dot \theta = 4kt, α=\ddot \theta = 4k##. Since the function of ##r## is dependent only on ##cos(kt^2)## i gues what's in front must be the amplitude therefore the radius should be ##R=p/2##? Is this correct thinking?
The velocity and acceleration are ##v=wR=2pkt, a=Rα=2pk##, i can find the the ##a_n=8pk^2t^2## but how do i find the velocity at that point. Kinda stuck on that?