   # Review. A 4.00-m length of light nylon cord is wound around a uniform cylindrical spool of radius 0.500 m and mass 1.00 kg. The spool is mounted on a frictionless axle and is initially at rest. The cord is pulled from the spool with a constant acceleration of magnitude 2.50 m/s 2 . (a) How much work has been done on the spool when it reaches an angular speed of 8.00 rad/s? (b) How long does it take the spool to reach this angular speed? (c) How much cord is left on the spool when it reaches this angular speed? ### Physics for Scientists and Enginee...

9th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305116399

#### Solutions

Chapter
Section ### Physics for Scientists and Enginee...

9th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305116399
Chapter 10, Problem 10.67AP
Textbook Problem
324 views

## Review. A 4.00-m length of light nylon cord is wound around a uniform cylindrical spool of radius 0.500 m and mass 1.00 kg. The spool is mounted on a frictionless axle and is initially at rest. The cord is pulled from the spool with a constant acceleration of magnitude 2.50 m/s2. (a) How much work has been done on the spool when it reaches an angular speed of 8.00 rad/s? (b) How long does it take the spool to reach this angular speed? (c) How much cord is left on the spool when it reaches this angular speed?

(a)

To determine

The work done on the spool when it reaches an angular speed of 8.00rad/s2 .

### Explanation of Solution

Given info: The length of the cord is 4.00m . The mass and radius of the spool is 1.00kg and 0.500m respectively. The initial speed of the spool is 0 . The acceleration of the spool is 2.50m/s2 . The final angular acceleration is 8.00rad/s2 .

Write the expression of the work done on the spool.

W=12I(ωf2ωi2) (1)

Here,

I is the moment of inertia of the disk.

ωf is the final angular speed.

ωi is the initial angular speed.

The moment of inertia of the disk is,

I=12mR2

Here,

m is the mass of the spool.

R is the radius of the spool.

Substitute 12mR2 for I in equation (1)

(b)

To determine

The time taken by the spool to reach this angular speed.

(c)

To determine

The amount of cord that is left on the spool.

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