Newton did such a good job with his laws of motion, that they still work even when objects move in circles.
Newton did such a good job with his laws of motion, that they still work even when objects move in circles. (1:29 )Centripetal force is just the net external force acting on an object that moves in a circle.(2:29) Episode 11 explores centripetal force with three examples - a rollerblading physics teacher, (2:59) a roller coaster vertical loop, (5:06) and enjoying a tire swing (7:25).
The Question of the Day asks: (10:01)
If you increase the mass of a car making a turn on level road, then how will the maximum velocity around the turn change?
a) there will be no change, the mass cancels
b) the max velocity will increase
c) the max velocity will decrease
Thank you for listening to The APsolute RecAP: Physics 1 Edition!
(AP is a registered trademark of the College Board and is not affiliated with The APsolute RecAP. Copyright 2020 - The APsolute RecAP, LLC. All rights reserved.)
Website:
EMAIL:
Follow Us:
Hi and welcome to the APsolute RecAP: Physics 1 Edition. Today’s episode will focus on uniform circular motion.
Lets Zoom out:
Unit 3 – Circular Motion and Gravitation
Topic 3.6-3.8
Big Idea – Force Interactions
Regardless of what you may think, thrill rides are only thrilling because of the accelerations you experience on the ride. You may think it is because you have a lot of velocity, but you move quicker in a car or an airplane usually, and frankly even sitting at your desk at school on Earth while hurtling through space. Those motions don’t usually feel particularly exciting until you are accelerating. Whether you are speeding up, slowing down, or turning… you are accelerating. Remember, acceleration is any change in velocity, and velocity is both speed and direction. Think of any fun amusement ride you’ve been on. My guess is you have come up with an image of a ride that fits one of those characteristics of accelerated motion.
Let’s Zoom in:
Newton did such a good job with his laws of motion, that they still work even when objects move in circles. It turns out that objects that move in a circle are accelerated inward toward the center of the circular path they are making. This acceleration is known as centripetal acceleration, and results from the fact that the direction of the velocity vector at any given moment is different from the previous moment. Unsurprisingly, we call an object’s linear velocity as it makes a circle the tangential velocity. The centripetal acceleration ends up being equal to the tangential velocity squared and then divided by the radius of the circular motion. Like any acceleration, if you multiply the mass of the object by the centripetal acceleration you get the net force acting on that object.
We have a special name for the net force on an object in circular motion - it is called the centripetal force. This is not to be confused with centrifugal force, a fictitious force that makes you feel like you are being pushed toward the door of your car when you make a very tight turn. Of course, you know that Newton’s 1st Law still holds true and your car door is actually pushing you in towards the center of the turn to change your forward velocity’s direction. Centripetal force is not a new force, it is just the net force from before. But instead of causing a linear acceleration, it is causing the object to move in a circular path at a particular radius and velocity.
Let’s look at your physics teacher skating on a pair of roller blades in a local roller derby league. They are skating around a turn with a radius of 10 m at the maximum possible speed. The combination of the wheels with the roller rink floor have a coefficient of static friction equal to 1.0. To find the maximum speed your teacher can barrel around the turn, we should first draw a free body diagram. Your teacher should have gravitational force acting downward, normal force acting upward, and static friction acting in the direction of the turn. Since there is no acceleration in the y-direction, normal force is equal to the weight (m*g). Frictional force is an unpaired force which is equal to the net force in the x-direction, and must then be your centripetal force. So, we can set the product of the coefficient of friction and the normal force (m*g in this case) equal to the centripetal force equation of mass*velocity squared over the radius. We find that your teacher can skate at a maximum velocity of 9.9 m/s.
Another good example of circular motion is when you are on a roller coaster and travel through a vertical loop. Assuming the loop you travel through is perfectly circular and you maintain a constant speed throughout the process, it can be treated in a similar manner. I am an especially big fan of the top portion of the loop when you feel weightless. Obviously you are not weightless, since you are still pretty close to earth’s surface, but it definitely feels like you are lighter. This because you are feeling the normal force acting on your body decrease. In fact, with what we now know about forces, you could probably figure out how fast you would have to travel so that you “feel” half your normal weight when traveling through a loop with a 15 m radius. That is, how quickly would you need to travel at the top of the loop so that you have a normal force equal to half of your weight (m*g). This time, there is a pair of forces acting, normal force and the gravitational force. Let’s stick to the convention that up is positive and downward is negative. Usually, you are inverted in your seat with these roller coasters, so we will say that at the top of the loop, you have negative m*g from gravity AND negative m*g/2 since you want to feel half your weight. They sum to yield -3/2 m*g for the net force, which we can set equal to the centripetal force equation m*v2/r. Masses cancel, radius is multiplied over and we arrive at a velocity of 14.8 m/s. You should notice that we need to make the centripetal force equation negative as well since it must act inward toward the center of circular motion, and while at the top that direction is downward.
What normal force would you experience at the bottom of the same loop traveling at the same speed? Most of the setup for the problem is the same, but this time the centripetal force is upward so that it still points toward the center of the circular path. We now would see that the normal force is also in the positive direction and has a value of 24.4 times your mass. That’s about 2.5 times gravity’s effects along. You know the normal mass * 9.8 m/s2?
Finally, you may have found yourself swinging an object in circles hanging from a long string and when rotating the object on the string, it sweeps out a conical shape. As our Physics 1 author Ryan watch’s his daughters play on their tire swing, and they do this for hours and hours, one of them sits on the tire while the other one takes a running start with the tire and then hops on to set the tire in this circular motion. This is known as a conical pendulum due to its very repeatable motion. There are only two forces acting on the tire swing as it sweeps around and around. The gravitational force and the tension force. The tension acts at an angle from vertical while gravitational force acts downward. Have you noticed that the faster the object rotates in its conical path, the larger the angle gets from vertical? They are somehow related. Knowing the length of rope he installed for the tire swing, and approximating the radius of the circle his daughters swing with to be 3 meters, he was able to determine that the angle from vertical for the tension is about 10 degrees. The combined mass of his daughters and the tire is 50 kg. With what you know now, you should be able to determine the velocity at which his girls are moving within their circular path. Draw the free-body diagram, and you’ll see that the y-component of the tension must be equal to weight (m*g). The x-component of tension is the only force acting in that direction and is therefore the centripetal force and the two can be set equal. You should find that the x-component of tension is equal to m*g times tangent of 10 degrees. This can be set equal to the equation for centripetal force, and wouldn’t you know it… masses cancel! After some algebra, you come to the conclusion that his daughter’s have a linear velocity of 2.25 m/s.
To Recap…
Newton’s Laws can be applied to objects in circular motion too. Centripetal force is just the net external force acting on an object that moves in a circle. By determining the net force acting on objects moving around curves or in circular paths and setting it equal to the centripetal force equation, it is possible to determine the object’s velocity, the radius of its motion, its mass, and many, many other things like coefficient of friction and apparent weight.
Coming up next on the APsolute RecAP Physics 1 Edition, we will look at some truly out of this world applications of circular motion when we look at gravitation.
Today’s Question of the Day focuses on uniform circular motion.
Question: If you increase the mass of a car making a turn on level road, then how will the maximum velocity around the turn change?
a) there will be no change, the mass cancels
b) the max velocity will increase
c) the max velocity will decrease