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# CP CALC A disk of radius 25.0 cm is free to turn about an ISBN: 9780321675460 31

## Solution for problem 65P Chapter 9

University Physics | 13th Edition

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Problem 65P

CP CALC? A disk of radius 25.0 cm is free to turn about an axle perpendicular to it through its center. It has very thin but strong string wrapped around its rim, and the string is attached to a ball that is pulled tangentially away from the rim of the disk (?Fig. P9.59?). The pull increases in magnitude and produces an acceleration of the ball that obeys the equation a(t) = At, where t is in seconds and A is a constant. The cylinder starts from rest, and at the end of the third second, the ball’s acceleration is 1.80 m/s2. (a) Find A. (b) Express the angular acceleration of the disk as a function of time. (c) How much time after the disk has begun to turn does it reach an angular speed of 15.0 rad/s? (d) Through what angle has the disk turned just as it reaches 15.0 rad/s? (?Hint:? See Section 2.6.)

Step-by-Step Solution:

Solution 65P Introduction First we have to find out the constant A, from this we can find out the linear acceleration as a function of time. From this functional form we can calculate the rotational acceleration as a function of time. Then we have to calculate the angular velocity and displacement after given time. Step 1 The linear acceleration is given by a(t) = At 2 Now at t = 3 s we have a = 1.80 m/s , hence we have 2 A = t = 13.00 ss = 0.600 m/s 3 Hence the constant A is given by 0.600 m/s 3. Step 2 Now the linear acceleration of the edge of the disc will be equal to the linear acceleration of the ball, which is given by a(t) = (0.600 m/s )t Now the angular acceleration is given by 3 = a(t)= (0.600 m/s )= (2.40 rad.s )t3 r (25.0×102m)

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##### ISBN: 9780321675460

University Physics was written by and is associated to the ISBN: 9780321675460. The full step-by-step solution to problem: 65P from chapter: 9 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. This full solution covers the following key subjects: disk, ball, acceleration, string, angular. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. This textbook survival guide was created for the textbook: University Physics, edition: 13. The answer to “CP CALC? A disk of radius 25.0 cm is free to turn about an axle perpendicular to it through its center. It has very thin but strong string wrapped around its rim, and the string is attached to a ball that is pulled tangentially away from the rim of the disk (?Fig. P9.59?). The pull increases in magnitude and produces an acceleration of the ball that obeys the equation a(t) = At, where t is in seconds and A is a constant. The cylinder starts from rest, and at the end of the third second, the ball’s acceleration is 1.80 m/s2. (a) Find A. (b) Express the angular acceleration of the disk as a function of time. (c) How much time after the disk has begun to turn does it reach an angular speed of 15.0 rad/s? (d) Through what angle has the disk turned just as it reaches 15.0 rad/s? (?Hint:? See Section 2.6.)” is broken down into a number of easy to follow steps, and 155 words. Since the solution to 65P from 9 chapter was answered, more than 270 students have viewed the full step-by-step answer.

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