Rotational Velocity and Acceleration

AI Thread Summary
Electric toothbrushes effectively remove dental plaque, with one model featuring a 1.1 cm diameter head that rotates back and forth through a 70-degree angle at 7600 RPM. The discussion focuses on calculating the angular acceleration in rad/sec² and the tangential acceleration in m/s² of the bristles. Clarifications were made regarding the size of the toothbrush, correcting an initial misunderstanding about its dimensions. Participants engaged in determining the period for one cycle based on the toothbrush's rotation frequency. The conversation highlights the importance of precise measurements and calculations in understanding the toothbrush's performance.
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1. Electric toothbrushes can be effective in removing dental plaque. One model consists of a head 1.1 cm in diameter that rotates back and forth through a 70.0 angle 7600 times per minute. The rim of the head contains a thin row of bristles. (See the figure )Assuming that the toothbrush has constant angular acceleration in each of the directions it turns, find the angular acceleration (in rad/sec2 ) of the rotating head and the tangential acceleration (in m/s2 ) of the bristles.


What is the rotational acceleration in rad/sec2

What is tangental accelration in m/s2
 
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Seriously? A toothbrush 1.1 inches in diameter? Is it for horses?
 
gneill said:
Seriously? A toothbrush 1.1 inches in diameter? Is it for horses?

Oops. that should say 1.1 cm
 
PhysicsScrub said:
Oops. that should say 1.1 cm

Phew! You had me worried for a moment there :smile:

So assuming that the brush goes from zero to angle seventy degrees in a half period, what is the required angular acceleration?
 
gneill said:
Phew! You had me worried for a moment there :smile:

So assuming that the brush goes from zero to angle seventy degrees in a half period, what is the required angular acceleration?

realllly unsure bud
 
Well, if it goes back and forth 7600 times every minute, what's the period for one cycle?
 

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