Part A Assume that the function (t) represents the length of tape that has unwou

Question

Part A Assume that the function (t) represents the length of tape that has unwound as a function of time. Find 0(t), the angle through which the drum will have rotated, as a function of time Express your answer (in radians) in terms of x(t) and any other given quantities Learning Goal To understand that contact between rolling objects and what they roll against imposes constraints on the change in position(velocity) and angle (angular velocity) View Available Hint(s) The way in which a body makes contact with the world often imposes a constraint relationship between its possible rotation and translational motion. A ball rolling on a road, a yo-yo unwinding as it falls, and a baseball leaving the pitcher's hand are all examples of radians Figure ? 1of2 Submit Part B The tape is now wound back into the drum at angular rate w(t). With what velocity will the end of the tape move? (Note that our drawing specifies that a positive derivative of x(t) implies motion away from the drum. Be careful with your signs! The fact that the tape is being wound back into the drum implies that w(t)

Explanation / Answer

A) Tape that has been unwound in one revolution = 2?*r where r is the radius.

so ?(t) = 2?*r / r

  ?(t) = x(t) / r

B) w(t) = d?(t)/ dt

puttin ?(t) from first part, we get

w(t) = dx(t) / dt

w(t) = v(t)

as v = rw

so, v(t) = rw(t)

D)  as motion is clockwise,

w = - vx / r

E) Using similar motion, and using the relation between linear(a) and angular acceleration(?) we get

ax = - r?

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