You toss a frisbee to your friend. It flies in a more-or-less straight line at a

Question

You toss a frisbee to your friend. It flies in a more-or-less straight line at a constant speed, reaching your friend after about 3 seconds. You estimate that when you released the frisbee, it was spinning around at a rate of about 6 rev/s (revolutions per second). You guess that the air drag slows the rate at which the frisbee spins by about 0.5 rev/s^2. You'd like to figure out how many revolutions the frisbee makes by the time your friend catches it.

Your friend is about 13 meters away when he catches the frisbee. Estimating that the frisbee is basically a spinning disc whose total mass is about 200 grams, how much energy is transferred to your friend on catching the frisbee? The frisbee's radius is about 15 cm.

Explanation / Answer

As

theta = wo t + 1/2 alpha t^2

and

theta = 15.75 rev = 98.96 rad

alpha = 0.5 rev/s^2 = -3.1416 rad/s^2

Then, as t = 3.0 s,

wo = 37.70 rad/s

Thus, when it reached the friend,

wf = wo + alpha t = 28.27 rad/s

As

I = 1/2 m r^2

Then

KEf = 1/2 I wf^2 = 0.8994 J [ANSWER, how much energy]

*********************************

Also,

T = I wf / t = 0.3635 N*m   [ANSWER, torque]

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