Mary is an avid game show fan and one of the contestants on a popular game show. she spins the wheel, and after 5.5 revolutions, the wheel comes to rest on a space that has a $1500 value prize. if the initial angular speed of the wheel is 3.80 rad/s, find the angle through which the wheel has turned when the angular speed reaches 2.40 rad/s.

Answer

or

Explanation:

Let the initial angular velocity be and the angular deceleration be . Equation (1) is the equivalent of the third equation of motion for a uniformly accelerated or decelerate linear motion for circular or angular motion, since the radius of the motion specified by the problem does not change.

where is the final angular velocity and is the angle turned through.

Also equation (2) is a relationship between angular velocity and number of revolution n;

Substituting equation (2) into (1) we obtain the following;

In the problem, our first mission is find the value of . When Mary spins the wheel with an initial angular velocity of 3.8rad/s, it comes to rest after making 5.5 revolutions. Therefore;

It should be noted that the wheel comes to rest that is why the final angular velocity

The angular acceleration is obtained by making the subject of formula from equation (3)

hence;

The negative result is an indication that the wheel is actually decelerating.

We then use equation (1) to determine the angle turned through when its angular velocity is 2.4rad/s as follows by making the subject of formula.

In this case,

Therefore;

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s