As a marble with a diameter of 2 cm rolls down an incline, its center moves with

Question

As a marble with a diameter of 2 cm rolls down an incline, its center moves with a linear acceleration of 3.4m/s^2. What is the angular acceleration of the marble? What is the angular speed of the marble after it rolls for 1.6 s from rest? An electrician of mass 50 kg is sitting on a pole of mass 2000 kg and length 10 m. The pole begins to fall full-length. The electrician decides to stick to the top of the pole as the pole swings down. What will be his/her velocity right before he/she hits the ground? A uniform crate with a mass of 16.18 kg rests on a platform with a coefficient of static friction equal to 0.573. The crate is a uniform cube with sides 1.22 m in length, What horizontal force applied to the top of the crate initiate tipping? Show why this force will tip the crate

Explanation / Answer

1) angular acc. = linear acc. / R

angular acc, alpha = 3.4m/s^2 / 0.02m = 170 rad/s^2

b) using wf = wi + alpha*t

wf = 0 + (170 * 1.6)   = 272 rad/s

2) this is system contains pole and man.

as pole come to ground, centre of mass pole comes down 5m and centre of mass of man comes down

to 10m .

using energy consewrvation,

mgh = I w^2

(2000 x 10 x 5) + ( 50 x 10 x 10) = (( 2000 x 10^2 / 3) + (50 x 10^2)) w

w = 105000 / 71666.67 = 1.465 rad/s

v = wr = 1.465 x 10   = 14.65 m/s

please don't post multiple questions at a time.

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