Question

A rider on a mountain bike is traveling to the left in the figure. Each wheel has an angular velocity of +25.1 rad/s, where, as usual, the plus sign indicates that the wheel is rotating in the counterclockwise direction. (a) To pass another cyclist, the rider pumps harder, and the angular velocity of the wheels increases from +25.1 to +29.1 rad/s in a time of 3.50 s. (b) After passing the cyclist, the rider begins to coast, and the angular velocity of the wheels decreases from +29.1 to +15.2 rad/s in a time of 10.7 s. Concepts: (i) Is the angular acceleration positive or negative when the rider is passing the cyclist and the angular speed of the wheels is increasing? positive negative Correct: Your answer is correct. (ii) Is the angular acceleration positive or negative when the rider is coasting and the angular speed of the wheels is decreasing? positive negative Correct: Your answer is correct. Calculations: In both instances, (a) and (b), determine the magnitude and direction of the angular acceleration (assumed constant) of the wheels. (Indicate the direction with the sign of your answer.) αa = rad/s2 αb = rad/s2

Answer 1

for (a) , wo=25.1 rad/secwf= 29.1rad/sec

t= 3.5 seconds

wf= wo+α_a t

29.1= 25.1 +α_a (3.5)

(29.1- 25.1)/3.5=α_a

α_a= 1.143 rad/s²

for (b)

wo=29.1 rad/secwf= 15.2 rad/sec

t= 10.7seconds

wf= wo+α_b t

15.2= 29.1 +α_b (3.5)

(15.2- 29.1)/10.7=α_b

α_b= -1.299 rad/s²