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A dog is running around a stationary turntable, with angular velocity w = 0.750 rad/s. The dog sees a bone 1/3 rev away. At that instant, the turntable begins to turn with angular velocity w = 0.015 rad/s.

a) How long will the dog take to reach the bone?

b) If the dog overshoots the bone, and continues around the moving turntable, how long before he reaches the bone once again.

Measure all times from the point at which the turntable starts to move.

I thought I would solve this in the frame of the turntable, which makes it quite simple, but I get different answers from those supplied on the my sheet.

Speed of dog in frame of turntable:

w = 0.750 rad/s - 0.0150 rad/s = 0.735 rad/s

Then I use theta = wt.

Bone is 1/3 revolution away:

t = theta/w = (2 pi/3)/0.735 = 2.85 s

Time once around the turntable:

t = (2 pi)/0.735 = 8.55 s

Add these two to get total time from start back to bone: 11.4 s

Answers on the handout are 2.88 s for the time to the bone, and 12.8 seconds for the time to come back around once again.

Seems a little large for rounding errors.

I thought ignoring the acceleration might be the problem, but there isn't enough information to calculate that.

Well, thanks for any pointers.

Dorothy