A computer disk starts from rest and it is given a constant positive angular acc

Question

A computer disk starts from rest and it is given a constant positive angular acceleration so that within 3 seconds its angular velocity increases from zero to 3 revolutions per second. The radius of the disk is 0.1 m. a) Calculate the magnitude of the total acceleration of a point P at the outer edge of the disc after 2 seconds. b) What is the direction and magnitude of the tangential velocity vector of point P after 2.0 s? Assume that at t=0 the angular position of point P is =0. c) What is the angle between the total acceleration vector and the velocity vector of a point on the outer rim of the disk at the moment when its angular speed is 6.0 rad/s?

Explanation / Answer

in 3 sec it goes from 0 to 3 revolution /sec

R = 0.1

a) in 2 sec angular velocity = 2 revolution/sec

=> A_r = 2*pi*2*pi*0.1 = 3.947 m/s^2

=> A_t = angular acc*R = 2*pi*0.1 = 0.628 m/s^2

=> magnitude = sqrt(3.947*3.947 + 0.628*0.628) = 3.996 m/s^2

b) V = omega*R = 2*2*pi*0.1 = 1.256 m/sec

angle = 0.5*2*pi*2*2 = 12.56 rad Answer

c) => A_r = 6*6*0.1 = 3.6 m/s^2

=> A_t = angular acc*R = 2*pi*0.1 = 0.628 m/s^2

V_t = 6*0.1 = 0.6

=> angle = arccos(0.6*0.628/(sqrt(3.6*3.6 + 0.628*0.628)*0.6) = 1.398 rad

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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