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Solved: CALC A uniform disk with radius R = 0.400 m and
Chapter 9, Problem 62P(choose chapter or problem)
Problem 62P
CALC A uniform disk with radius R = 0.400 m and mass 30.0 kg rotates in a horizontal plane on a frictionless vertical axle that passes through the center of the disk. The angle through which the disk has turned varies with time according to θ(t) = (1.10 rad/s)t + (6.30 rad/s2)t2. What is the resultant linear acceleration of a point on the rim of the disk at the instant when the disk has turned through 0.100 rev?
Questions & Answers
QUESTION:
Problem 62P
CALC A uniform disk with radius R = 0.400 m and mass 30.0 kg rotates in a horizontal plane on a frictionless vertical axle that passes through the center of the disk. The angle through which the disk has turned varies with time according to θ(t) = (1.10 rad/s)t + (6.30 rad/s2)t2. What is the resultant linear acceleration of a point on the rim of the disk at the instant when the disk has turned through 0.100 rev?
ANSWER:
Solution 62P
Step 1:
Provided, 𝜽 (t) = 1.10 rad/s t + (6.30 rad/s2) t2
Take the first derivative of 𝜽 with respect to time and it will give you the angular velocity,
𝜽’ (t) = 1.10 rad/s + (12.60 rad/s2) t
Take the second derivative of 𝜽 with respect to time and it will give you the angular acceleration,
𝜽” (t) = 0 + (12.60 rad/s2)
Therefore, tangential acceleration, a = 12.60 rad/s2