You will need
• angular velocity, tangential acceleration
Instruction
1
From the definition of angular acceleration, it follows that for its calculation it is necessary to know the angular velocity. The angular velocity vector modulo equal to the angle of rotation of the body per unit time: v = df/dt, where v is the angular velocity, df is the angle of rotation.
The angular velocity vector will be directed by the rule of thumb along the rotation axis, i.e. in the direction in which is screwed the gimlet with right-hand thread, if revolved in the same direction.
2
Since the angular acceleration describes the rate of change of angular velocity, then by definition, it is equal to the modulo: a = dv/dt = (d^2)f/d(t^2).Thus, the angular acceleration in this sense is similar to linear, only the second derivative with respect to time is taken of the angular velocity, not linear.
3
Find now direction of the vector angular acceleration. Obviously, it will be directed along the axis of rotation. If the magnitude of the vector is greater than zero, that is, the body will accelerate, then the vector a is directed in the same direction as the angular velocity vector. If this value is negative and the body slows down,then the vector is directed in the opposite direction.
4
Angular acceleration can also be expressed by the formula: a = At/R. In this formula, At is the tangential acceleration, and R is the radius of curvature of the trajectory. Tangential acceleration is a full component of linear acceleration directed along the tangent to the trajectory. Do not confuse it with a normal (or centripetal) accelerationm which is directed toward the center of curvature of the trajectory.