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Unformatted text preview: 623 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 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ T 1 whereas linear velocity has dimensions ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ T L . ( b ) True. The angular velocity of all points on the wheel is d θ / dt. ( c ) True. The angular acceleration of all points on the wheel is d ω / dt. 3 •• Picture the Problem The constant-acceleration equation that relates the given variables is θ α ω ω ∆ + = 2 2 2 . 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 2 ω . Using a constant-acceleration equation, relate the initial and final angular velocities to the angular acceleration: θ α ω ω ∆ + = 2 2 2 or, because 2 ω = 0, θ α ω ∆ = 2 2 Let ∆ θ 10 represent the number of revolutions required to reach an angular velocity ω : 10 2 2 θ α ω ∆ = (1) Let ∆ θ 2 ω represent the number of revolutions required to reach an angular velocity ω : ( ) ω θ α ω 2 2 2 2 ∆ = (2) Divide equation (2) by equation (1) and solve for ∆ θ 2 ω : ( ) 10 10 2 2 2 4 2 θ θ ω ω θ ω ∆ = ∆ = ∆ Chapter 9 624 The number of additional revolutions is: ( ) rev 30 rev 10 3 3 4 10 10 10 = = ∆ = ∆ − ∆ θ θ θ and correct. is ) ( c *4 • Determine the Concept Torque has the dimension ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 2 2 T ML . ( a ) Impulse has the dimension ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ T ML . ( b ) Energy has the dimension ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 2 2 T ML . correct. is ) ( b ( c ) Momentum has the dimension ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ T ML . 5 • Determine the Concept The moment of inertia of an object is the product of a constant that is characteristic of the object’s distribution of matter, the mass of the object, and the square of the distance from the object’s center of mass to the axis about which the object is rotating. Because both ( b ) and ( c ) are correct correct. is ) ( d *6 • Determine the Concept Yes. A net torque is required to change the rotational state of an object. In the absence of a net torque an object continues in whatever state of rotational motion it was at the instant the net torque became zero. 7 • Determine the Concept No. A net torque is required to change the rotational state of an object. A net torque may decrease the angular speed of an object. All we can say for sure is that a net torque will change the angular speed of an object....
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This note was uploaded on 08/18/2010 for the course IMT 12253 taught by Professor Mikael during the Spring '10 term at École Normale Supérieure.
- Spring '10