Non-Uniform circular motion

Circular motion Uniform circular motion refers to circular motion with Constant tangential velocity Acceleration ALWAYS directed toward the center of the circle Only ONE force is acting on the rotating object

Non-Uniform So what happens if you turn that circle 90o so that it is vertical?

More than 1 force Now you will have more than one force involved. Take, for example, a ball swung around in a vertical circle.

Label the forces

Which force is winning? In order for the ball to stay in the circular path, there must be a NET FORCE directed toward the center of the circular path. So, which force is winning? TENSIONAL FORCE Which force is losing? FORCE OF WEIGHT

WRITE AN EQUATION Winning Force – Losing Force = NET Force The NET force is the CENTRIPETAL FORCE It is the force you are ACTUALLY experiencing while in the circular motion

Re-write the complete equation FT – FW = FC FW = mg FC = mv2/r FT – mg = mv2/r

A student attaches a ball to the end of a string 0 A student attaches a ball to the end of a string 0.796m in length and then swings the ball in a vertical circle. The speed of the ball is 9.11 m/s at its lowest point.  a. Find the centripetal acceleration at its lowest point. b. If the ball has a mass of .25kg, what is the tension in the string? 104.26 m/s2 28.5 N

2. A 22 kg child sits in a swing supported by a rope 1. 6m long 2. A 22 kg child sits in a swing supported by a rope 1.6m long. If the tension at the lowest point is 272N, find the child’s speed at the lowest point. 2.03 m/s

What if the object is at the top of the vertical circle? Draw your force diagram

Which force is winning? NEITHER!! THEY ARE ON THE SAME TEAM!!!

Now your equation becomes: FT + FW = FC FT + mg = mv2/r

You can see the IMPORTANCE of drawing a force diagram for these problems!!! vs.

Also think about types of forces Different types of forces can be delivering the force required to keep an object in the circular motion (Do NOT confuse with NET force) We will encounter Tension and Normal Force in non-uniform circular motion

3. A student attaches a. 25kg ball to the end of a string 0 3. A student attaches a .25kg ball to the end of a string 0.796m in length and then swings the ball in a vertical circle. The speed of the ball is 4.03 m/s at its highest point. a. What is the tensional force at the top of the circle? 2.65 N

A test pilot has a mass of 60kg A test pilot has a mass of 60kg. When she is flying an upside down loop of radius 1000m at a speed of 200 m/s, with what force does her seat press on her? (Remember, she is upside down.) BTW – what is the name of the force is keeping her in the loop? **DRAW A FORCE DIAGRAM** NORMAL FORCE 1812 N

What is different about this situation? 5. A pail of water of mass 2.98 kg is rotated in a vertical circle of radius 2.2 m. What is the minimum speed of the pail at the top of the circle if no water is to spill out? What is different about this situation? The tensional force will be ZERO!

5. A pail of water of mass 2.98 kg is rotated in a vertical circle of radius 2.2 m. What is the minimum speed of the pail at the top of the circle if no water is to spill out? 4.64 m/s

6. A bowling ball is attached to a 2 6. A bowling ball is attached to a 2.3 m rope that swings in a pendulum-type manner. At the bottom of the arc, the speed of the ball is 1.85 m/s, and the tension is 80 N. What is the mass of the bowling ball? 7.09 kg