A disk with mass m = 10.9 kg and radius R = 0.37 m begins at rest and accelerate

Question

A disk with mass m = 10.9 kg and radius R = 0.37 m begins at rest and accelerates uniformly for t = 18.3 s, to a final angular speed of ? = 32 rad/s. ( i know the answers but i need someone to expalin some parts to me)

1)What is the tangential component of the acceleration of a point on the rim of the disk when the disk has accelerated to half its final angular speed?

Answer: i used the formula tangential acceleration=R*angular acceleration and got 0.64699 which is the right answer, but i was wondering, do we just ignore the part which says "has accelerated to half its final angular speed"?? i thought i should use the constant angular accleration formula: angular velocity=angular acceleration*time again, but this time i should divide angular velocity by 2 here(just like the question asks), then plug the angular acceleration that i get from this equation into my first equation, but i got the wrong answer. why doesnt the second method work??

2)What is the magnitude of the radial component of the acceleration of a point on the rim of the disk when the disk has accelerated to half its final angular speed?

Answer: radial acceleration=(angular velocity)^2*R , so how come they divide angular velocity by 2 in this question, but not the last question??

Explanation / Answer

1)
w = w0 + alpha t
so
alpha = w/t=32/18.3

so a tangent = alpha r = 32*0.37/18.3=0.647

2) a radial = w^2 R

we want the speed when we are at half of max so, w = 32/2 = 16

so a radial = 16^2 *0.37=94.72 m/s^@

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.