Fill in the following table of straight line vs rotational analogs: Linear displ

Question

Fill in the following table of straight line vs rotational analogs: Linear displacement x Linear velocity v = delta x/delta t Linear acceleration a = delta v/delta t Angular displacement theta Angular velocity w = Angular acceleration a = If an object goes some angle theta around a circle, what fraction of the way around does it go? If it also goes a distance x around the circle, express the fractional distance around the circle in terms of the distance x and the circumference. How are the linear distance around the circle (x) and the angular distance (theta) related? How are the linear velocity v and the angular velocity w related? How are the linear acceleration and the angular acceleration related?

Explanation / Answer

arc length = theta*radius

x = theta*R

theta = x/R

circumference c= 2*piR

R = c/2*pi

theta = x/c/2*pi

theta = 2*pi*x/c

v = Rw

w = d(theta)/dt

w = 2*pi/c*dx/dt

v = R*2pi/c*dx/dt

v = R*theta*dx/dt

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