Tangential acceleration happens at the bodies moving on a curvilinear trajectory. It is directed in the direction of change of speed of a body on a tangent to a trajectory of the movement. Tangential acceleration does not happen at the bodies evenly moving on a circle, they possess only centripetal acceleration.
It is required to you
- - speedometer or radar;
- - ruler or roulette;
- - stop watch.
Instruction
1. Find tangential acceleration of aτ if full acceleration of the point moving on a curvilinear trajectory of an and its centripetal acceleration of an is known. For this purpose from a square of full acceleration take away a square of centripetal acceleration, and take the square root aτ= from the received value √ (a²-an²). If centripetal acceleration is unknown, but there is a value of instantaneous velocity, measure by a ruler or a roulette the radius of curvature of a trajectory and find its value, having divided a square of instantaneous velocity of v which measure by a speedometer or the radar on the radius of curvature of a trajectory of R, an=v²/R.
2. Example. The body moves on a circle with a radius of 0.12 m. Its full acceleration is equal to 5 m/s², define its tangential acceleration, at the moment when its speed is equal to 0.6 m/s. At first find centripetal acceleration of a body at the specified speed, for this purpose its square divide into an trajectory radius = v²/R = 0.6²/0.12=3 m/s². Find tangential acceleration on a formula aτ= √ (a²-an²)= √ (5²-3²)= √ (25-9) = √16=4 m/s².
3. Determine the size of tangential acceleration through change of the module of speed. For this purpose determine the initial and final speed of a body for some period which measure by means of a stop watch by a speedometer or the radar. Find tangential acceleration, having taken away initial value of speed v0 from final v and having divided into a period of t for which this change happened: aτ = (v-v0)/t. If the value of tangential acceleration turned out negative, so the body slows down if positive – accelerates.
4. Example. For 4 about the speed of the body moving on a circle decreased from 6 to 4 m/s. Define its tangential acceleration. Having applied a settlement formula, receive aτ = (v-v0)/t= (4-6)/4=-0,5 m/s². It means that the body slows down with acceleration absolute value of which equally in 0.5 m/s².