Question

For this problem, we’ll assume that you are at the United State Embassy when Superman slows Earth. By my clock, it took Superman about 10 seconds to bring Earth from its initial angular speed (7.27*10^-5) to its final angular velocity of zero. Let’s assume that your initial angular velocity is positive, because when viewed from above the North pole, you move counterclockwise (i.e., we travel eastward).

(a)     During the 10 seconds, what was your angular acceleration (including sign), whichwe’ll assume to be constant? Solve it algebraically and then numerically. Include units.

Would you call this a “big” number or a “small” number?

(b)    During the 10 seconds, what was your tangential acceleration? Algebraically thennumerically.

Would you call this a “big” number or a “small” number?

(c)     During the 10 seconds, through how many radians did you travel?

(d)    During the 10 seconds, how many meters did you travel?

Answer 1

Units not given,

wi = 7.27 x 10^-5 ; wf = 0 ;

a)We know from eqn of circular motion

wf = w0 + alpha t

alpha = (wf - w0)/t

alpha = [0 -(7.27 x 10^-5)]/10 = -7.27 x 10^-6 rad/s^2

Hence, alpha = -7.27 x 10^-6 rad/s^2

b)we know that the inesr acceleration is related to angular acceleration as:

a = R aplha

a = 6.37 x 10^6 x -7.27 x 10^-6 = -46.31 m/s^2

Hence, a = -46.31 m/s^2

c)We know from eqn of motion

theta = wi t + 1/2 alpha t^2

theta = 7.27 x 10^-5 x 10 - 0.5 x 7.27 x 10^-6 x 10^2 = 3.64 x 10^-4rad

Hence, theta = 3.64 x 10^-4 rad

d)D = r theta

D = 6.37 x 10^6 x 3.64 x 10^-4 = 23.19 x 10^2 m

Hence, 23.19 x 10^2 m