   Chapter 7, Problem 17P

Chapter
Section
Textbook Problem

(a) What is the tangential acceleration of a bug on the rim of a 10.0-in.-diameter disk if the disk accelerates uniformly from rest to an angular velocity of 78.0 rev/min in 3.00 s? (b) When the disk is at its final speed, what is the tangential velocity of the bug? One second after the bug starts from rest, what are its (c) tangential acceleration, (d) centripetal acceleration, and (e) total acceleration?

a)

To determine
The tangential acceleration of the bug.

Explanation

Given Info The diameter of the disk is 10.0in , the disk accelerates from rest to 78.0revmin-1 in time 3.00s .

Explanation:

The tangential acceleration of the disk is,

at=rα

• r is the radius of the disk
• α is the angular acceleration of the disk

The angular acceleration of the disk is given by,

α=ωfωit

• ωf is the final angular velocity
• ωi is the initial angular velocity
• t is the time taken

Using (1) the tangential acceleration of the disk is,

at=r(ωfωit)

In terms of diameter of the disk the tangential acceleration will be,

at=(d2)(ωfωit)

• d is the diameter of the disk.

Substitute 10.0in for d , 78.0revmin-1 for ωf , 0 for ωi , 3

b)

To determine
The tangential velocity when the disk is at its final angular speed.

c)

To determine
The tangential acceleration one second after the bug starts from rest.

d)

To determine
The centripetal acceleration of the bug one second after the bug starts from rest.

e)

To determine
The total acceleration of the bug one second after the bug starts from rest.

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