Question: A uniform 5-kg disk has a radius of 0.12 and is pivotedso that it rota

Question

Question: A uniform 5-kg disk has a radius of 0.12 and is pivotedso that it rotates freely about its axis. A string wrapped aroundthe disk is pulled with a force equal to 20 N.

a. what is the torque being exerted by this force about therotation axis?
b. what is the angular acceleration of the disk?
c. if the disk starts from rest what is the angular speed after 5seconds?
d. what is the kinetic energy after 5 seconds?
e. what is the angular displacement of the disk during the 5seconds?
f. show all the work done by the torque, equals to the kineticenegry.

Explanation / Answer

T(orque) = F R = 20 * .12 = 2.4 N-m I = 1/2 M R2 = 2.5 * .122 = .036 kgm2 = T / I = 2.4 / .036 = 66.7 / s2 = t = 66.7 * 5 = 333 / s KE = 1/2 I 2 = (.036 / 2)* 3332 = 1996 J = 1/2 t2 = (66.7 / 2) * 25 = 834deg T = 1/2 I 2 = 1996 as foundabove T = 2.4 * 834 =2001       Agrees withinrounding = t = 66.7 * 5 = 333 / s KE = 1/2 I 2 = (.036 / 2)* 3332 = 1996 J = 1/2 t2 = (66.7 / 2) * 25 = 834deg T = 1/2 I 2 = 1996 as foundabove T = 2.4 * 834 =2001       Agrees withinrounding

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