Honors Physics
Angular Kinematic Equations
Work Sheet #2
1.
MC The angular acceleration in circular motion (a) is equal in magnitude to the tangential acceleration divided by the radius, (b)
increases the angular velocity if both angular velocity and angular acceleration are in the same direction, (c) has units of s 2 , (d)
all of the preceding.
2.
MC In circular motion, the tangential acceleration (a) does not depend on the angular acceleration, (b) is constant, (c) has units
of s 2 , (d) none of these.
3.
MC For uniform circular motion, (a)   0, (b)   0, (c) r  0, (d) none of the preceding.
4.
CQ A car increases its speed when it is on a circular track. Does the car have centripetal acceleration? How about angular
acceleration? Explain.
5.
CQ Is it possible for a car traveling on a circular track to have angular acceleration, but not centripetal acceleration? Explain. n
6.
CQ Is it possible for a car traveling on a circular track to have an increase in tangential acceleration and not centripetal
acceleration?
7.
 During an acceleration, the angular speed of an engine increases from 600 rpm to 2500 rpm in 3.0 s. What is the average
angular acceleration of the engine?
8.
 A merry-go-round accelerating uniformly from rest achieves its operating speed of 2.5 rpm in five revolutions. What is the
magnitude of its angular acceleration?
9.
 To maintain their bone density and other vital bodily signs, the inhabitants of a cylindrically shaped living space want to
generate a “1-g environment” on their way to a distant destination. Assume the cylinder has a diameter of 250 m (they live on
the inner surface) and is initially not rotating about its long axis. For minimal disruption, the (constant) angular acceleration is a
2
very gentle 0.00010 rad s . Determine how long it takes for them to reach their goal of a “1-g environment.”
10.
IE  A car on a circular track accelerates from rest. (a) The car experiences (1) only angular acceleration, (2) only centripetal
acceleration, (3) both angular and centripetal accelerations. Why? (b) If the radius of the track is 0.30 km and the magnitude of
2
the constant angular acceleration is 4.5 103 rad s , how long does the car take to make one lap around the track? (c) What is
the total (vector) acceleration of the car when it has completed half of a lap?
11.
 The blades of a fan running at low speed turn at 250 rpm. When the fan is switched to high speed, the rotation rate increases
uniformly to 350 rpm in 5.75 s. (a) What is the magnitude of the angular acceleration of the blades? (b) How many revolutions
do the blades go through while the fan is accelerating?
12.
 In the spin-dry cycle of a modern washing machine, a wet towel with a mass of 1.50 kg is “stuck to” the inside surface of
the perforated (to allow the water out) washing cylinder. To have decent removal of water, damp/wet clothes need to experience
a centripetal acceleration of at least 10g. Assuming this value, and that the cylinder has a radius of 35.0 cm, determine the
constant angular acceleration of the towel required if the washing machine takes 2.50 s to achieve its final angular speed.
ANSWERS
1.
2.
3.
4.
5.
6.
4.
d
d
a
yes, yes
no,
no
7. 66.3 rad/s2
8. 1.1 x 10-3 rad/s2
9. 2.8 x 103s
10.
11. (a) 1.82 rad/s2, (b) 28.7 rev
12. 6.69 rad/s2
Yes , a car in circular motion always has centripetal acceleration.
Yes , it also has angular acceleration as its speed is increasing.
5.
No , this is not possible. As long as the car is traveling around the circular track, it always has centripetal acceleration.
10.
(a) The answer is (3) both angular and centripetal accelerations . There is always centripetal acceleration for any car in
circular motion. When the car increases its speed on a circular track, there is also angular acceleration.
(b) Given: o = 0,  = 4.5  103 rad/s2,  = 1 rev = 2 rad. Find: t.
2
2(2 rad)
 = o t + 12  t 2 = 0 + 12  t 2,  t =
=
= 53 s .

4.5  103 rad/s2
Pearson, Wilson, bufa, Lou 6th edition