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rotates counterclockwise in a horizontal plane, accelerating uniformly A disk 15

ID: 1401303 • Letter: R

Question

rotates counterclockwise in a horizontal plane, accelerating uniformly A disk 15 cm in diameter from 33 rpm to 45 rpm in min a. What is the angular acceleration of the disk? (5) a 1, men Go s 5 33 12 APM b. What is the angular speed of the disk 30 s after it starts to accelerate? (5) C. What is the tangential speed of a point on the edge of the disk 30 s after it starts to accelerate? (5) 30 APM v o. 612 d. What are the tangential and radial components of the acceleration of a point on the edge of the disk 30 s after it starts to accelerate? Draw the components at the point shown on the diagram disregard scale). (10) e. Through how many rotations does the disk turn while accelerating from 33 rpm to 45 rpm? (5) 33 rpm lo as apr

Explanation / Answer

given,

diameter = 15 cm

initial angular velocity = 33 rpm or 3.456 rad/sec

final angular velocity = 45 rpm or 4.712 rad/sec

time = 1 min or 60 sec

acceleration = change of velocity / time

acceleration = 4.712 - 3.456 / 60

angular acceleration = 0.0206 rad/sec^2

by first equation of motion

final angular velocity = initial angular velocity + angular acceleration * time

final angular velocity = 3.456 + 0.0206 * 30

final angular velocity after 30 sec = 4.047 rad/sec

tangential speed = angular speed * radius

tangential speed = 4.047 * (0.15 / 2)

tangential speed = 0.303525 m/s

tangential acceleration = angular acceleration * radius

tangential acceleration = 0.0206 * (0.15 / 2)

tangential acceleration = 0.001545 m/s^2

radial acceleration = velocity^2 / radius

radial acceleration = 0.303525^2 / (0.15 / 2)

radial acceleration = 1.228 m/s^2