A bucket in an old well is hoisted upward by a rope which winds up on a cylinder having a radius of 0.050 m. How many rev/s must the cylinder turn if the bucket is raised at a speed of 0.15 m/s?
a. 3.0 rev/s
b. 1.5 rev/s
c. 0.48 rev/s
d. 0.24 rev/s
[Ques. 2] The end of the cutting cord on a gas-powered weed cutter is 0.21 m in length. If the motor rotates at the rate of 20 rev/s, what is the tangential speed of the end of the cord?
a. 13 m/s
b. 4.2 m/s
c. 26 m/s
d. 2.7 m/s
[Ques. 3] A 0.150-m-radius grinding wheel starts at rest and develops an angular speed of 12.00 rad/s in 7.80 s. What is the average tangential acceleration of a point on the wheel's edge?
a. 0.231 m/s2
b. 1.54 m/s2
c. 10.3 m/s2
d. 14.0 m/s2
[Ques. 4] A point on the rim of a 0.30-m-radius rotating wheel has a tangential speed of 5.0 m/s. What is the tangential speed of a point 0.20 m from the center of the same wheel?
a. 1.0 m/s
b. 0.50 m/s
c. 3.3 m/s
d. 17 m/s
[Ques. 5] Suppose a wheel is initially rotating at 10.0 rad/s while undergoing constant angular acceleration reaching a speed of 30.0 rad/s after 36.0 seconds have elapsed. How long after the initial time has the wheel undergone half of the angular displacement that it will have gone through during the entire 36.0-second interval?
a. 0.556 s
b. 22.2 s
c. 18.0 s
d. 56.5 s
[Ques. 6] Starting from rest, a wheel undergoes constant angular acceleration for a period of time T. At which of the following times does the average angular acceleration equal the instantaneous angular acceleration?
a. 0.50T
b. 0.67T
c. 0.71T
d. all of the above
[Ques. 7] Starting from rest, a wheel undergoes constant angular acceleration for a period of time T. At what time after the start of rotation does the wheel reach an angular speed equal to its average angular speed for this interval?
a. 0.25T
b. 0.50T
c. 0.67T
d. 0.71T
[Ques. 8] A 0.30-m-radius automobile tire rotates how many rad after starting from rest and accelerating at a constant 2.0 rad/s2 over a 5.0-s interval?
a. 12.5 rad
b. 25 rad
c. 2.0 rad
d. 0.50 rad
[Ques. 9] A Ferris wheel, rotating initially at an angular speed of 0.500 rad/s, accelerates over a 10.4-s interval at a rate of 0.040 0 rad/s2 . What angular displacement does the Ferris wheel undergo in this 10.4-s interval?
a. 7.4 rad
b. 0.21 rad
c. 2.2 rad
d. 0.0019 rad
[Ques. 10] A Ferris wheel, rotating initially at an angular speed of 0.50 rad/s, accelerates over a 7.0-s interval at a rate of 0.040 rad/s2 . What is its angular speed after this 7.0-s interval?
a. 0.20 rad/s
b. 0.30 rad/s
c. 0.46 rad/s
d. 0.78 rad/s
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