How Fast Do Bristles on an Electric Toothbrush Move?

In summary, an electric toothbrush with a head diameter of 1.10 cm, rotating back and forth through a 70.0 degree angle at a rate of 7600 times/min, has an average angular speed of 310 rad/sec. The average linear speed of the bristles against the teeth is approximately 1.85 m/s.
  • #1
merlos
14
0
Electric toothbrushes can be effective in removing dental plaque. One model consists of a head 1.10 cm in diameter that rotates back and forth through a 70.0 degree angle 7600 times/min. The rim of the head contains a thin row of bristles.

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Part A: What is the average angular speed in each direction of the rotating head, in rad/sec?

(140degrees)(pi/180) = 2.44 rad/rev

w = (7600 rev/min)(1min/60sec)(2.44rad/1rev) = 310 rad/sec


Part B What is the average linear speed in each direction of the bristles against the teeth?

A little unsure of

v = rw
v = (.006m)(310rad/sec)
v = 1.85 m/s
 
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  • #2
Your method looks OK. To avoid round-off errors in your arithmetic, don't round off until the very last step.
 

Related to How Fast Do Bristles on an Electric Toothbrush Move?

1. What is the difference between linear and angular quantities?

Linear quantities are measurements that involve straight lines, while angular quantities involve rotational motion. Linear quantities are typically measured in units such as meters, feet, or miles, while angular quantities are measured in degrees or radians.

2. Can linear and angular quantities be converted to each other?

Yes, linear and angular quantities can be converted to each other using mathematical formulas. For example, to convert from degrees to radians, you would multiply the degree measurement by π/180. Similarly, to convert from radians to degrees, you would multiply the radian measurement by 180/π.

3. How are linear and angular quantities related?

Linear and angular quantities are related by a concept called rotational motion. This means that when an object moves in a circular motion, it is simultaneously experiencing both linear and angular motion. The rate at which an object moves in a circular motion is measured in angular quantities.

4. What are some real-world examples of linear and angular quantities?

Linear quantities can be seen in everyday measurements such as the distance a car travels or the length of a pencil. Angular quantities can be observed in the rotation of a bicycle wheel, the movement of a clock's hands, or the spinning of a top.

5. How are linear and angular quantities used in scientific research?

Linear and angular quantities are commonly used in scientific research to study the movement and motion of objects. They are important in fields such as physics, engineering, and astronomy, where precise measurements of distance, speed, and angles are necessary for experiments and calculations.

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