What is the tangential acceleration of a bug on the rim of a 78 rpm record of di

Question

What is the tangential acceleration of a bug on the rim of a 78 rpm record of diameter 6.4 in. if the record moves from rest to its final angular speed in 7 s? The conversion between inches and meters is 0.0254 m/in. Answer in units of m/s^2 .

When the record is at its final speed, what is the tangential velocity of the bug? Answer in units of m/s.

What is its radial acceleration 2.2 s after starting from rest? Assume that the record has constant angular acceleration. Answer in units of m/s^2 .

This question is a repost.. need correct explanation! Thanks!

Explanation / Answer

convert angular speed from rpm to rev/s

w = 78 rpm ( 2 pi/ 60) = 8.164 rad/s

r = d/2 = 6.4 in /2 = 3.2 in ( 0.0254 m/ in) = 0.08128 m

angular acccleration is

wf -wi = alpha t

alpha = wf- wi/t

tangential accleration is

a_t = r alpha = r (wf- wi/t ) = 0.08128 m( 8.164 rad/s)/ 7s = 0.094 m/s^2

tangential velocity is

v_t = r w =0.08128 m( 8.164 rad/s) = 0.663 m/s

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since recored has constant angualr accleration and starts frm rest

w = alpha t = ( w_f/t_f ) t

radial accleration is

a_r = w^2 r = ( ( w_f/t_f ) t)^2 r = 0.08128 m (( 2.2 s)( 8.164 rad/s)/ 7s)^2 = 0.5349 m/s^2

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