   Chapter 7, Problem 12P

Chapter
Section
Textbook Problem

A 45.0-cm diameter disk rotates with a constant angular acceleration of 2.50 rad/s2. It starts from rest at t = 0, and a line drawn from the center of the disk to a point P on the rim of the disk makes an angle of 57.3° with the positive x-axis at this time. At t = 2.30 s, find (a) the angular speed of the wheel, (b) the linear speed and tangential acceleration of P, and (c) the position of P (in degrees, with respect to the positive x-axis).

(a)

To determine
The angular speed of the wheel.

Explanation

Given info: The diameter of the disk is 45.0cm . The angular acceleration of the wheel is 2.50rads-2 . The initial time is t=0 and final speed is t=2.30s . A line drawn from the centre of the disk makes an angle of 57.3° with the positive x-axis at time t=2.30s .

Explanation:

The angular velocity at any time t is given by,

ω=ω0+αt

• ω0 is the initial velocity
• α is the angular acceleration
• ω is angular velocity at time t

Substitute 0 for ω0 , 2

(b)

To determine
The linear speed of the point P.

(c)

To determine
The position of P .

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