Awheel accelerates uniformly from rest to an angular speed of 25 rad/s in 10 s.(a) find the angular acceleration of the wheel. (b) find the tangential and radial acceleration of a point 10cm from the wheel’s center. (c) how many revolutions has the wheel turned during this time interval? (d) then, find the wheel’s angular deceleration if it comes to a full stop after 5 rev

(a) Angular acceleration

The initial angular speed of the wheel is , the final angular speed is , and the time taken is t=10 s. Therefore, the angular acceleration of the wheel is given by:

(b1) Tangential acceleration

The tangential acceleration is given by the product between the angular acceleration and the distance from the wheel's center r. In this case,  and , therefore the tangential acceleration is

b2) Radial acceleration

The radial acceleration (also called centripetal acceleration) is given by:

where is the final angular speed while r=0.1 m is the distance from the center of the wheel. Substituting numbers, we get

c) Number of revolutions

First of all, we need to find the angle covered during this time interval, which is given by:

And keeping in mind that , the number of revolutions made is:

d) Deceleration

In this last part of the problem, we are told that the wheel comes to a stop after . We also know the initial angular speed, , and the final angular speed, , so we can find the new angular (de)celeration by using the equation:

Substituting numbers, we get