College Physics

10 ROTATIONAL MOTION AND ANGULAR MOMENTUM Figure 10.1The mention of a tornado conjures up images of raw destructive power. Torna ...

10 Rotational Motion and Angular Momentum Why do tornadoes spin at all? And why do tornados spin so rapidly? The answer is that ...

whereΔωis thechange in angular velocityandΔtis the change in time. The units of angular acceleration are(rad/s)/s, orrad/s^2. If ...

Figure 10.4In circular motion, linear accelerationa, occurs as the magnitude of the velocity changes:ais tangent to the motion. ...

Example 10.2 Calculating the Angular Acceleration of a Motorcycle Wheel A powerful motorcycle can accelerate from 0 to 30.0 m/s ...

The magnitude of angular acceleration isαand its most common units arerad/s 2 . The direction of angular acceleration along a fi ...

In these equations, the subscript 0 denotes initial values (θ 0 ,x 0 , andt 0 are initial values), and the average angular veloc ...

Solution for (d) The number of meters of fishing line isx, which can be obtained through its relationship withθ: x=rθ=(0.0450 m) ...

θ=x (10.30) r. Solving this equation forxyields x=rθ. (10.31) Before using this equation, we must convert the number of revoluti ...

As always, it is necessary to convert revolutions to radians before calculating a linear quantity likexfrom an angular quantity ...

Figure 10.11An object is supported by a horizontal frictionless table and is attached to a pivot point by a cord that supplies c ...

4. Applynet τ = Iα, α =net τ I , the rotational equivalent of Newton’s second law, to solve the problem. Care must be taken to u ...

Strategy Angular acceleration is given directly by the expressionα=net τ I : α=τ (10.45) I . To solve forα, we must first calcul ...

Figure 10.14The motor works in spinning the grindstone, giving it rotational kinetic energy. That energy is then converted to he ...

netW=^1 (10.59) 2 Iω^2 −^1 2 Iω 02. This equation is thework-energy theoremfor rotational motion only. As you may recall, net wo ...

Figure 10.17A large grindstone is given a spin by a person grasping its outer edge. Solution for (b) To findωfrom the given info ...

rotational kinetic energy of the blades by losing altitude and aligning the blades so that the helicopter is spun up in the desc ...

(10.81) h= 1 2 Iω 2 mg = 5.26×10^5 J ⎛ ⎝1000 kg ⎞ ⎠ ⎛ ⎝9.80 m/s 2 ⎞ ⎠ = 53.7 m. Discussion The ratio of translational energy to ...

Assuming no losses due to friction, there is only one force doing work—gravity. Therefore the total work done is the change in k ...

Analogy of Rotational and Translational Kinetic Energy Is rotational kinetic energy completely analogous to translational kineti ...