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Example Questions
Example Question #51 : Centripetal Force And Acceleration
It takes a disc player seconds to get up to its speed of rotations per second, what is the angular acceleration of the disc player in radians?
Similar to linear acceleration, angular acceleration is related to the angular velocity by the following
from here we simply plug in our values of and to get . Next to convert to radians we take the relations that pi is equal to rotation and multiply our by to arrive at our final answer of
Example Question #52 : Centripetal Force And Acceleration
You decide to ride an attraction at the fair; it is a circular, flat, ride that spins very fast; so fast, that it's nearly impossible to fall to the ground. Riders "stick" to the walls when the ride hits its top speeds.
Let's say the attraction spins in a clockwise manner. While riding the attraction, toward which direction is the centripetal (net) force pointing?
Outward
Inward
Against motion (counter clockwise)
With motion (clockwise)
Inward
Most of the success for this ride experience can be credited to Newton's Third Law. It states that if object 1 exerts onto object 2, then object 2 must be exerting a force . They are equal and opposite forces, called an action reaction pair. This concept applies when you're typing on your cell phone. when you touch down on your screen or button, your finger doesn't go through the phone, right? The phone is sending back an equal force to you which prevents your finger from going through the screen.
The same thing applies on the attraction. Your body is pushing outward on the walls of the ride. If no centripetal force was present, your body would project on a tangent as depicted in the diagram below. However, centripetal force is present. This is the force that is countering your body; it is pushing you towards the center. Now as we know, centripetal force isn't ever drawn on a diagram because it is a "net" force, or a collection of forces. But what we do know is that during circular motion, centripetal force (and acceleration) point towards the center.
During the ride, your body is trying to follow the tangental paths shown, but the reciprocal force, , is keeping your body stationary on the wall. The wall is following a circular path, which makes you follow the circular path. This action reaction pair is what allows the attraction to work. Centripetal force points inwards.
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