Rotacional

Rotation

1* · Two points are on a disk turning at constant angular velocity, one point on the rim and the other halfway between

the rim and the axis. Which point moves the greater distance in a given time? Which turns through the greater angle?

Which has the greater speed? The greater angular velocity? The greater tangential acceleration? The greater angular

acceleration? The greater centripetal acceleration?

1. The point on the rim moves the greater distance. 2. Both turn through the same angle. 3. The point on the rim has

the greater speed 4. Both have the same angular velocity. 5. Both have zero tangential acceleration.

6. Both have zero angular acceleration. 7. The point on the rim has the greater centripetal acceleration.

2 · True or false: (a) Angular velocity and linear velocity have the same dimensions. (b) All parts of a rotating wheel

must have the same angular velocity. (c) All parts of a rotating wheel must have the same angular acceleration.

(a) False (b) True (c) True

3 ·· Starting from rest, a disk takes 10 revolutions to reach an angular velocity w. At constant angular acceleration,

how many additional revolutions are required to reach an angular velocity of 2w? (a) 10 rev

(b) 20 rev (c) 30 rev (d) 40 rev (e) 50 rev.

From Equ. 9-9; w 2 µ q q2 = 4q1; Dq = 3q1 = 30 rev; (c)

4 · A particle moves in a circle of radius 90 m with a constant speed of 25 m/s. (a) What is its angular velocity in

radians per second about the center of the circle? (b) How many revolutions does it make in 30 s?

(a) w = v/r

(b) q = wt

w = (25/90) rad/s = 0.278 rad/s

q = 8.33 rad = 1.33 rev.

5* · A wheel starts from rest with constant angular acceleration of 2.6 rad/s2. After 6 s, (a) What is its angular

velocity? (b) Through what angle has the wheel turned? (c) How many revolutions has it made? (d) What is the speed

and acceleration of a point 0.3 m from the axis of rotation?

(a) w = at

(b), (c) q = 1/2at2

(d) v = wr, ac = rw 2, at = ra; a = (at

2+ac

2)1/2

w = (2.6 ´ 6) rad/s = 15.6 rad/s

q = 46.8 rad = 7.45 rev

v = (15.6 ´ 0.3) m/s = 4.68 m/s;

a =[(0.3 ´ 15.62)2 + (0.3 ´ 2.6)2]1/2 m/s2 = 73 m/s2

Chapter 9 Rotation

6 · When a turntable rotating at 33 1/3 rev/min is shut off, it comes to rest in 26 s. Assuming constant angular acceleration,

find (a) the angular acceleration, (b) the average angular velocity of the turntable, and (c) the number of revolutions

it makes before stopping.

(a) a = w/t

(b) wav = 1/2w0

(c) q = wavt

a = (33.3 ´ 2p/60 ´ 26) rad/s2 = 0.134 rad/s2

wav = 1/2(33.3 ´ 2p/60) rad/s = 1.75 rad/s

q = (1.75 ´ 26) rad = 45.4 rad = 7.22 rev

7 · A disk of radius 12 cm, initially at rest, begins rotating about its axis with a constant angular acceleration of 8

rad/s2. At t = 5 s, what are (a) the angular velocity of the disk, and (b) the tangential acceleration at and the centripetal

acceleration ac of a point on the edge of the disk?

(a) w = at

(b) at = ra; ac = rw 2

w = (8 ´ 5) rad/s = 40 rad/s

at = (0.12 ´ 8) m/s2 = 0.96 m/s2;

ac = (0.12 ´ 402) m/s2 = 192 m/s2

8 · Radio announcers who still play vinyl records have to be careful when cuing up live recordings. While studio

albums have blank spaces between the songs, live albums have audiences cheering. If the volume levels are left up

when the turntable is turned on, it sounds as though the audience has suddenly burst through the wall. If a turntable

begins at rest and rotates through 10o in 0.5 s, how long must the announcer wait before the record reaches the

required angular

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