I need help with number 1. Show all steps in your solutions, beginning with the

Question

I need help with number 1. Show all steps in your solutions, beginning with the appropriate equations from the ions handout sheet. Include diagrams wherever appropriate. A solid cylinder with 20.0 cm radius and 16.5 kg mass is accelerated in rotation around its central axis from rest to 275 rev / min. The cylinder turns 3.60 revolutions during the uniform angular acceleration, caused by a tangential force acting on the rim of the cylinder. Find the magnitude of this tangential force. A uniform hollow cylinder with 8.00 cm outer radius, 5.50 cm inner radius, and 16.5 kg mass is at the top of an incline as shown, at a height h above the horizontal floor. The cylinder rolls (without slipping) from rest down the incline, reaching a center-of mass velocity of 7.25 m/s at the end of the incline. Find height h.

Explanation / Answer

Moment of Inertia cyllinder, I = (1/2)*M*R^2

= (1/2)*16.5*0.2^2

= 0.33 kg.m^2

w1 = 0

w2 = 275 rev/min

= 275*2*pi/60 rad/s

= 28.78 rad/s

angular dispalcement, theta = 3.6 rev

= 3.6*2*pi rad

= 22.61 rad
angular acceleration of cyllnder, alfa = (w2^2 - w1^2)/(2*theta)

= (28.78^2 - 0^2)/(2*22.61)

= 18.3 rad/s^2

now Apply, Torque = I*alfa

F*R = I*alfa

F = I*alfa/R

= 0.33*18.3/0.2

= 30.19 N

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