Lesson 11/11

Lesson 11/11

Centripetal Acceleration Continued

Until we get back from Thanksgiving

Zoom and Lesson in Google Classroom everyday

No, I'm not ill

I was just too close to someone who was.

Open Ended

Journal: What does the word centripetal mean?

Magnitude of Acceleration

• What is the magnitude of an objects centripetal acceleration?

• Centripetal acceleration always points to the center of the circle. Its magnitude is equal to the squar of the speed divided by the radius of motion.

• So...

•  $a_c\ =\frac{v^2}{r}$  

Magnitude of Acceleration

• a_c is specifically centripetal acceleration.

Period of Revolution

• One way to describe the speed of an objexxt moving in a circle is to measure its Period (T), the time needed for the object to make on complete revolution.

• During this time, the object travels a distance equal to the circumference of the circle (2 $\pi$  r in radians).  The speed, then is represented by  $v=\frac{\left(2\pi r\right)}{T}$  

Period of Revolution

• If you substitute v in the equation for centripetal acceleration, you obtain the following equation.

•  $a_c=\ \frac{\left(\frac{2\pi r}{T}\right)^2}{r}^{ }=\ \frac{4\pi^2r}{T^2}$  

Centripetal Force

• Because the acceleration of an object moving in a circle is always in the direction of the net force acting on it, there must be a net force toward the center of the circle.

• The net force toward the center of the circle is called centripetal force.

• To accurately analyze centripetal acceleration situations, you must identify the agent of the force that causes the acceleration. Then you can apply Newton's 2nd law for the component in the direction of the acceleration.

Newton's Second Law for Circular Motion

• The net force on an object moving in a circle is equal to the object's mass times the centripetal acceleration.

• F_net = ma_c

Direction of acceleration

• For circular motion, the direction of the acceleration is always toward the center of the circle. It is labeled tang for tangential.

• You will apply Newton's second law in these directions, just like we have done before.

• Remember that centripetal force is just another name for the net force in the centripetal direction. It is the sum of all the real forces that act upon the centripetal axis.

• When an object in uniform circular motion is released, it flies off in the direction of its velocity.

Open Ended

Example Problem: A 13 g rubber stopper is attached to 0.93 m string. The stopper is swung in a horizontal circle, making one revolution in 1.18 s. Find the magnitude of the tension force exerted by the string on the stopper.

Practice Problems in Google Classroom.

Open Ended

Using school appropriate language, how ready are you for this Covid situation to be over?