Question

A beetle with a mass of 25.0 g is initially at rest on the outer edge of a horizontal turntable that is also initially at rest. The turntable, which is free to rotate with no friction about an axis through its center, has a mass of 80.0 g and can be treated as a uniform disk. The beetle then starts to walk around the edge of the turntable, traveling at an angular velocity of 0.0700 rad/s clockwise with respect to the turntable. (b) With respect to you, motionless as you watch the beetle and turntable, what is the angular velocity of the beetle? Use a positive sign if the answer is clockwise, and a negative sign if the answer is counter-clockwise. rad/s (c) What is the angular velocity of the turntable (with respect to you)? Use a positive sign if the answer is clockwise, and a negative sign if the answer is counter-clockwise. rad/s (d) If a mark is placed on the turntable at the beetle's starting point, how long does it take the beetle to reach the mark again?

Answer 1

With respect to you, motionless as you watch the beetle and turntable, what is the angular velocity of the beetle

just use conservation of angular momentum

Let beetle be denoted as 1 and turntable be denoted as 2

the relative angular velocity of beetle as we look at it

w1 = w2 + w

as per conservation of angular momentum

I1w1 = I2w2

I1 ( w2 + w) = I2w2

w1 = I2w / I1 + I2

for disk, I = 1/2mr² and for beetle as point mass, I = mr²

as the radius is same for both , we get

w1 = m2w / (2m1 + m2)

w1 = 80e-3 * 0.07 / (2 * 25e-3 + 80e-3)

w1 = 0.043 rad/sec

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What is the angular velocity of the turntable (with respect to you)

just use the relative angular velocity formula which we used above

w2 = 0.07 - 0.043

w2 = 0.027 rad/sec

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If a mark is placed on the turntable at the beetle's starting point, how long does it take the beetle to reach the mark again

1 full circle ( revolution ) means 2 radians

t = distance / speed

t = 2 / 0.07

t = 89.75 sec