A cylinder rotating about its axis with a constant angular acceleration of 1.8 r

Question

A cylinder rotating about its axis with a constant angular acceleration of 1.8 rad/s^2 starts from rest at t=0. At the instant it has turned through 0.4 radian, what is the magnitude of the total linear acceleration of a point on the rim (radius = 15 cm)? (Please show work)
A 0.41 m/s2 B 0.43 C 0.35 D 0.39 E 0.55 A cylinder rotating about its axis with a constant angular acceleration of 1.8 rad/s^2 starts from rest at t=0. At the instant it has turned through 0.4 radian, what is the magnitude of the total linear acceleration of a point on the rim (radius = 15 cm)? (Please show work)
A 0.41 m/s2 B 0.43 C 0.35 D 0.39 E 0.55
A 0.41 m/s2 B 0.43 C 0.35 D 0.39 E 0.55

Explanation / Answer

apply the relation between linear and angular coordinates as

a = r A

where A is angular acceleration

r is raidus

a is linear accleration

A = vectort sum of radial and tangential accleration

so

Arad = RW^2 = 2 A THeta

so

Arad =0.15* 2* 1.8 * 0.4

Arad = 0.216 m/s^2

A tan = rA = 1.8 * 0.15 = 0.27 m/s^2

total accleration a^2 = arad^2 + a tan^2

a^2 = 0.216^2 +0.27^2

a = 0.346 m/s^2 , answer is option C-----<<<ANswer

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