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 aprExplanation / 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
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