Teste

Chapter 9 Rotation
Conceptual Problems
*1 • Determine the Concept Because r is greater for the point on the rim, it moves the greater distance. Both turn through the same angle. Because r is greater for the point on the rim, it has the greater speed. Both have the same angular velocity. Both have zero tangential acceleration. Both have zero angular acceleration. Because r is greater for the point on the rim, it has the greater centripetal acceleration. 2 •

(a) False. Angular velocity has the dimensions ⎢ ⎥ whereas linear velocity has ⎣T ⎦ dimensions ⎢ ⎥ . T (b) True. The angular velocity of all points on the wheel is dθ/dt. (c) True. The angular acceleration of all points on the wheel is dω/dt. 3 •• Picture the Problem The constant-acceleration equation that relates the given variables 2 is ω 2 = ω0 + 2α∆θ . We can set up a proportion to determine the number of revolutions required to double ω and then subtract to find the number of additional revolutions to accelerate the disk to an angular speed of 2ω. Using a constant-acceleration equation, relate the initial and final angular velocities to the angular acceleration: Let ∆θ10 represent the number of revolutions required to reach an angular velocity ω: Let ∆θ2ω represent the number of revolutions required to reach an angular velocity ω: Divide equation (2) by equation (1) and solve for ∆θ2ω:
2 ω 2 = ω0 + 2α∆θ

⎡1⎤

⎡L⎤ ⎣ ⎦

2 or, because ω0 = 0,

ω 2 = 2α∆θ ω 2 = 2α∆θ10
(1)

(2ω)2 = 2α∆θ2ω

(2)

∆θ2ω =
623

(2ω)2 ∆θ ω2 10

= 4∆θ10

624 Chapter 9
The number of additional revolutions is:

4∆θ10 − ∆θ10 = 3∆θ10 = 3(10 rev ) = 30 rev and (c) is correct.

*4

•

Determine the Concept Torque has the dimension ⎢ (a) Impulse has the dimension ⎢

⎡ ML2 ⎤ . 2 ⎥ ⎣T ⎦

⎡ ML ⎤ . ⎣ T ⎥ ⎦ ⎡ ML2 ⎤ (b) Energy has the dimension ⎢ 2 ⎥ . ⎣T ⎦ ⎡ ML ⎤ . ⎣ T ⎥ ⎦

(b) is correct.

(c) Momentum has the dimension ⎢

5 • Determine the Concept The moment of inertia of an object is the