please with details thank you Four questions worth 5 marks each. Please provide

Question

please with details thank you

Four questions worth 5 marks each. Please provide answers with full work/justification. I. A vinyl record (diameter 12 inches) is spinning at 33 rpm and then the machine is turned off, causing it to slow down at a constant rate, coming to a stop in 5.0 seconds. Determine; a) the angular acceleration. b) the tangential acceleration of a point on the edge of the record. c) the tangential velocity of a point on the edge 3.0 seconds before it stops. d) the total angle (in radians) thorough which it turns as it stops. e) the number of revolutions through which it turns as it stops.

Explanation / Answer

a.) v = u + at

33 rpm = 33(2pi/60) rad/s = 3.456 rad/s

0 = 3.456 + a*(5)

So a = - 0.6912 rad/s^2

b.) tangential acc = a*r = -0.6912*6*0.0254 = -0.1053 m/s^2

c.) v = r*w

0 = w + - 0.6912*3

So w = 2.07345 rad/s

So v = 2.07345*6*0.0254 = 0.316 m/s

d.) v^2 - u^2 = 2as

0 - (3.456)^2 = 2(-0.6912)*s

SO s = 8.64 radians

e.) No.of Revolutions = 8.64/2pi = 1.375 revolutions

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