Question

A wheel starts from rest and rotates about its axis with constant angular acceleration. After 5.7 s have elapsed, it has rotated through an angle of 20 radians. What is the angular acceleration of the wheel? What is the angular velocity when the time t = 5.7 s? What is the centripetal acceleration of a point on the wheel a distance r = 0.35 m from the axis at t = 5.7 s?

Answer 1

Let the constant angular acceleration be , the angular displacement in time t = 5.7 s in . We will be using the equation,

Here initially, the angular velocity is zero, therefore the equation becomes,

Substituting, the values we get,

Now, we know that,

Substituting we get,

Hence the angular velocity at t = 5.7 s is 7.011 rad/s

The centripetal acceleration is given by,

The angular velocity at t = 5.7 s is 7.011 rad/s, and the point is at a distacent of r = 0.35 m, Substituting we get,