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The diameter of a DVD is approximately 12 centimetres. The drive motor of the DVD player is controlled to rotate precisely between 200 and 500 revolutions per minute, depending on what track is being read. (a) Find an interval for the angular speed of a DVD as it rotates. (b) Find an interval for the linear speed of a point on the outermost track as the DVD rotates.

Respuesta :

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(a) The angular speed of a DVD as it rotates is approximately between 2.094 radians per second and 5.236 radians per second.

(b) The linear speed of a point on the outermost track as the DVD rotates is approximately between 25.132 centimeters per second and 62.83 centimeters per second.

Explanation:

(a) The angular speed (ω) is calculated using the formula ω = 2πf, where f is the frequency of rotation in hertz. Given the range of revolutions per minute (200 to 500), the corresponding angular speed is between 2.094 and 5.236 radians per second.

(b) The linear speed (v) is determined by the formula v = rω, where r is the radius of the circular path and ω is the angular speed. Considering the outermost track with a radius of 6 centimeters (half of the diameter), the linear speed is between 25.132 and 62.83 centimeters per second.

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