A child abuses an antique record player to further his knowledge of physics. The

Question

A child abuses an antique record player to further his knowledge of physics. The record turntable can be treated as a uniform disk (I = .5MR^2) with mass 0.75 kg and radius 0.16 m that spins freely

1) First the child wraps a long string several times around the turntable's circumference. He then pulls horizontally on the string with a constant linear acceleration of 1.2 m/s^2, causing the turntable to begin rotating from rest. Assuming that the string doesn't slip, what angular speed will the turntable have once the child has pulled the end of the string a distance of 2.0 m?

2) Next the child drops a handful of spaghetti onto the turntable (the spaghetti sticks to the turntable). The child then observes that the rotation rate of the turntable is now 5.0 rad/s slower. Find the moment of inertia of the spaghetti about its rotation axis. If you didn't answer the previous part use a value of 12 rad/s for the initial angular velocity of the turntable (so it ends up at 7.0 rad/s).

3) To stop the spinning mess, the child could press his thumb against the turntable near the rotation axis or near the outer edge of the turntable. Which choice would result in the child needing to do the least amount of work to stop the turntable, or is it a tie? Justify your answer with a conceptual argument or a calculation.

Explanation / Answer

1.

vo = initial speed = 0 m/s

vf = final speed

a = 1.2 m/s2

d = distance travelled = 2 m

using the equation

vf2 = vo2 + 2 a d

vf2 = 02 + 2 (1.2) (2)

vf = 2.2 m/s

angular speed is given as

w = vf/r = 2.2/0.16 = 13.75 rad/s

2)

wi = 13.75 rad/s

wf = 8.75 rad/s

Id =moment of inertia of disk = (0.5) M R2 = (0.5) (0.75) (0.16)2 = 0.0096 kgm2

Is = moment of inertia of spaghetti = ?

using conservation of angular momentum

Id wi = (Id + Is) wf

(0.0096) (13.75) = (0.0096 + Is) (8.75)

Is = 0.0055 kgm2

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