Question

4 A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. When it has made 10 rev determine its angular velocity.]

Answer 1

Answer:

$w_f$= 22.41rad/s

Explanation:

First, we know that:

a = 4 rad/s^2

S = 10 rev = 62.83 rad

Now we know that:

$w_f^2-w_i^2=2aS$

where $w_f$ is the final angular velocity, $w_i$ the initial angular velocity, a is the angular aceleration and S the radians.

Replacing, we get:

$w_f^2-(0)^2=2(4)(62.83)$

Finally, solving for $w_f$:

$w_f$= 22.41rad/s

Answer 2

The rate of change of angular displacement is defined as angular velocity. The angular velocity will be 22.41rad/s.

What is angular velocity?

The rate of change of angular displacement is defined as angular velocity. Its unit is rad/sec.

ω = θ t

Where,

θ is the angle of rotation,

t is the time

ω is the angular velocity

The given data in the problem is;

u is the initial velocity=0

α is the angular acceleration =  4.0 rad/s²

t is the time period=

n is the number of revolution = 10 rev

From Newton's second equation of motion in terms of angular velocity;

$\rm \omega_f^2 - \omega_i^2 = 2as \\\\ \rm \omega_f^2 - 0 = 2\times 4 \times 62.83 \\\\ \rm \omega_f= 22.41 \ rad/sec$

Hence the angular velocity will be 22.41 rad/s.

To learn more about angular velocity refer to the link

https://brainly.com/question/1980605