Q3 A typical 45 rpm vinyl record had a about 17 8am and rotated at 45 rpm\'s dia

Question

Q3 A typical 45 rpm vinyl record had a about 17 8am and rotated at 45 rpm's diameter of clockwise (looking down on the record from above) 1rpm 1 revolution/minute (20ptsU a. If the record's needle is placed 6.50cm from the center of the revolving record, what it the "tangential" speed of the record just underneath the needle? side view top view b. If a piece of dust of mass, m 500 x 10 kg, also sits on the record at 6.50cm from the center of the revolving record, what is the magnitude and direction of the (4 pts) Fe,on the piece of dust? Drow an arrow to show the direction. c. The operator suddenly shuts the power off, and the record player comes to a full stop in 25.0s. What is the magnitude and direction of the "tangential acceleration of the record while the record player slows to a full stop? Draw an orrow to show the direction. pts.) d Through what rotation angle (in degrees) does the piece of dust rotate from the time the

Explanation / Answer

3. (a) v = w r

w = 45 rpm = 45 x 2pi rad / 60 sec

w = 4.71 rad/s

v = (4.71 rad/s) (0.065 m) = 0.306 m/s

(b) Fc = m v^2 / r

= (5 x 10^-4 ) ( 0.306^2) / (0.065)

= 7.22 x 10^-4 N

radially toward the center.

(c) wf = wi + alpha t

0 = 4.71 + 25 alpha

alpha = - 0.19 rad/s^2

magnitude = 0.19 rad/s^2

tangential acc = alpha r = 0.19 x 0.065 = 0.012 m/s^2

direction = tangentially counterclockwise direction

(d) theta = wi t + alpha t^2 /2

= (4.71 x 25) + (-0.19 x 25^2 / 2)

= 58.4 rad

theta (in degrees ) = 3344.64 deg

(e) wi = 4.71 rad/s

wf = -4.71 rad/s

- 4.71 = 4.71 + 45 alpha

alpha = - 0.21 rad/s^2

magnitude = 0.21 rad/s^2

counterclockwise

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