Rotational Kinematics Quiz #1
1) How many rad/s is 25 revolutions per minute equivalent to?
@ Use your knowledge of unit conversions for this problem:
25 rev/min 
0.1047 rad/s
 2.6 rad/s
1 rev/min
2) Angular displacement is usually express in units of
@ Angular displacement is measured in radians or degrees.
3) A boy and a girl are riding on a merry-go-round which is turning at a constant rate. The boy is
near the outer edge, and the girl is closer to the center. Who has the greater angular speed?
@ The angular speed is the same, but their linear speed would differ due to their radius.
4) The second hand of a clock has a length of 0.30 m. What distance does the tip of the second
hand sweep through in 3 minutes and 45 seconds?
@ The second hand goes around the clock 3.75 times in 3 minutes and 45 seconds making the
angle equal 3.75  2π rad . The distance traveled in that time is equal to:
x  rθ
x  (0.30 m)(7.5 π rad)
x  7.1 m
5) ) A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the outer rim move in
2.0 s?
@ First change revolutions per minute into radians per second:
1500 rev/min 
0.1047 rad/s
 157 rad/s
1 rev/min
The diameter is 26 cm so the radius is 13 cm or 0.13 m. The angular displacement in that time
equals:
θ  157 rad/s  2.0 s  314 rad
The linear displacement during that time is:
x  rθ
x  (0.13 m)( 314 rad)
x  41 m
6) A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is the linear speed of a
point 0.10 m from the center of the wheel?
@ The linear speed can be found:
v  2πrf
v  2π (0.10 m)(0.5 rev/s)
v  0.31 rad/s
7) A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/s. What is the
linear speed of a point on the wheel's rim?
@ The linear speed can be found:
v  rω
v  (1.0 m)( 2.0 rad/s)
v  2.0 m/s
8) A wheel accelerates with a constant angular acceleration of 4.5 rad/s2. If the initial angular
velocity is 1.0 rad/s, what is the angle the wheel rotates through in 2.0 s?
@ Use the angular kinematics equation:
θ  ω0 t 
1 2
αt
2
θ  (1.0 rad/s)(2.0 s) 
1
(4.5 rad/s 2 )( 2.0 s) 2
2
θ  11 rad
9) A wheel starts from rest and reaches an angular speed of 6.0 rad/s while turning through 2.0
revolutions. What is the average angular acceleration of the wheel?
@ Use the equation that has angular speed, angular displacement, and angular acceleration:
ω 2  ω02  2αθ
(6.0 rad/s) 2  0  2α (2.0 rev  2π )
36  2α (4π )
36
8π
α  1.4 rad/s 2
α
10) @ Use the equation that has linear speed, linear displacement, and linear acceleration:
v 2  v 02  2ax
(0) 2  (8.40 m/s) 2  2a (115 m)
0  71  230a
 71  230a
 71
a
230
a  0.31 m/s 2
Use linear acceleration to find angular acceleration:
a tan  rα
 0.31 m/s 2  (0.34 m) α
 0.31 m/s
0.34 m
α  0.91 rad/s 2
α