Angular Acceleration Quiz

PDF page 438: Angular velocity is not constant when a skater pulls in her arms, when a child starts up a merry-go-round from rest, or when a computer’s hard disk slows to a halt when switched off. In all these cases, there is an angular acceleration, in which changes. The faster the change occurs, the greater the angular acceleration. Angular acceleration is defined as the rate of change of angular velocity. In equation form, angular acceleration is expressed as follows:

PDF page 437: Uniform Circular Motion and Gravitation discussed only uniform circular motion, which is motion in a circle at constant speed and, hence, constant angular velocity. Recall that angular velocity was defined as the time rate of change of angle :

PDF page 437: where is the radius of curvature, also seen in Figure 10.3. According to the sign convention, the counter clockwise direction is considered as positive direction and clockwise direction as negative

PDF page 438: . If increases, then is positive. If decreases, then is negative.

PDF page 438: Suppose a teenager puts her bicycle on its back and starts the rear wheel spinning from rest to a final angular velocity of 250 rpm in 5.00 s. (a) Calculate the angular acceleration in . (b) If she now slams on the brakes, causing an angular acceleration of , how long does it take the wheel to stop? Strategy for (a)

PDF page 439: If the bicycle in the preceding example had been on its wheels instead of upside-down, it would first have accelerated along the ground and then come to a stop. This connection between circular motion and linear motion needs to be explored. For example, it would be useful to know how linear and angular acceleration are related. In circular motion, linear acceleration is tangent to the circle at the point of interest, as seen in Figure 10.4. Thus, linear acceleration is called tangential acceleration .

PDF page 439: context of circular motion, linear acceleration is also called tangential acceleration . Linear or tangential acceleration refers to changes in the magnitude of velocity but not its direction. We know from Uniform Circular Motion and Gravitation that in circular motion centripetal acceleration, , refers to changes in the direction of the velocity but not its magnitude. An object undergoing circular motion experiences centripetal

PDF page 439: If the bicycle in the preceding example had been on its wheels instead of upside-down, it would first have accelerated along the ground and then come to a stop. This connection between circular motion and linear motion needs to be explored. For example, it would be useful to know how linear and angular acceleration are related. In circular motion, linear acceleration is tangent to the circle at the point of interest, as seen in Figure 10.4. Thus, linear acceleration is called tangential acceleration .

PDF page 439: context of circular motion, linear acceleration is also called tangential acceleration . Linear or tangential acceleration refers to changes in the magnitude of velocity but not its direction. We know from Uniform Circular Motion and Gravitation that in circular motion centripetal acceleration, , refers to changes in the direction of the velocity but not its magnitude. An object undergoing circular motion experiences centripetal

PDF page 439: acceleration, as seen in Figure 10.5. Thus, and are perpendicular and independent of one another. Tangential

PDF page 440: FIGURE 10.5 Centripetal acceleration occurs as the direction of velocity changes; it is perpendicular to the circular motion. Centripetal

PDF page 439: context of circular motion, linear acceleration is also called tangential acceleration . Linear or tangential acceleration refers to changes in the magnitude of velocity but not its direction. We know from Uniform Circular Motion and Gravitation that in circular motion centripetal acceleration, , refers to changes in the direction of the velocity but not its magnitude. An object undergoing circular motion experiences centripetal

PDF page 440: These equations mean that linear acceleration and angular acceleration are directly proportional. The greater the angular acceleration is, the larger the linear (tangential) acceleration is, and vice versa. For example, the greater the angular acceleration of a car’s drive wheels, the greater the acceleration of the car. The radius also matters. For example, the smaller a wheel, the smaller its linear acceleration for a given angular acceleration .

PDF page 440: A powerful motorcycle can accelerate from 0 to 30.0 m/s (about 108 km/h) in 4.20 s. What is the angular acceleration of its 0.320-m-radius wheels? (See Figure 10.6.)