Uniform Circular Motion

The net acceleration can be expressed as the vector sum of the tangential acceleration and the centripetal acceleration . The centripetal acceleration is given by: Where:
- is the instantaneous speed of the ball,
- is the radius. Given:
- The tangential acceleration ,
- The angle between the net acceleration and the centripetal acceleration is . Using the relation for the net acceleration: Also, the net acceleration is related to the angle between the tangential and centripetal accelerations: Since , the tangent of the angle gives: This gives: Solving for : Now substitute the value of into the centripetal acceleration formula: Solving for :
Thus, the instantaneous speed is .