All AP Physics 1 Resources
Example Questions
Example Question #42 : Centripetal Force And Acceleration
An object has a mass M, velocity V, and moves in a circle with radius R.
What happens to the centripetal acceleration on the object when the velocity is doubled?
The centripetal acceleration of the object is quadrupled.
The centripetal acceleration of the object remains the same.
The centripetal acceleration of the object is halved.
The centripetal acceleration of the object goes to zero.
The centripetal acceleration of the object is doubled.
The centripetal acceleration of the object is quadrupled.
The equation for centripetal acceleration is:
Where is the centripetal acceleration on an object, is the velocity of an object, and is the radius in which the object moves in a circle.
The velocity has an quadratic relationship with centripetal acceleration, so when the velocity is doubled, the centripetal acceleration is quadrupled.
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.
Example Question #1 : Torque
A bolt connecting the main and rear frame of a mountain bike requires a torque of to tighten. If you are capable of applying of force to a wrench in any given direction, what is the minimum length of the wrench that will result in the required torque?
The minimum length of the wrench will assume that the maximum force is applied at an angle of . Therefore, we can use the simplified expression for torque:
Here, is the length of the wrench.
Rearranging for length and plugging in our values, we get:
Example Question #1 : Torque
A uniform rod of length 50cm and mass 0.2kg is placed on a fulcrum at a distance of 40cm from the left end of the rod. At what distance from the left end of the rod should a 0.6kg mass be hung to balance the rod?
50cm
42cm
The rod cannot be balanced with this mass
45cm
48cm
45cm
The counterclockwise and clockwise torques about the pivot point must be equal for the rod to balance. Taking the fulcrum as the pivot point, the counterclockwise torque is due to the rod’s weight, gravitational force acting downwards at the center of the rod. If we use the pivot as our reference, then the center of the rod is 15cm from the reference.
Set this equal to the clockwise torque due to the additional mass, a distance r to the right of the pivot.
.
Solving for r gives r = 0.05m to the right of the pivot, so 40 + 5 cm from the left end of the rod.
Example Question #1 : Torque
A 2kg mass is suspended on a rope that wraps around a frictionless pulley attached to the ceiling with a mass of 0.01kg and a radius of 0.25m. The other end of the rope is attached to a massless suspended platform, upon which 0.5kg weights may be placed. While the system is initially at equilibrium, the rope is later cut above the weight, and the platform subsequently raised by pulling on the rope.
What is the torque on the pulley when the system is motionless?
0N*m
9.8N*m
10N*m
19.6N*m
0N*m
The net torque on the pulley is zero. Remember that , assuming the force acts perpendicular to the radius. Because the pulley is symmetrical in this problem (meaning the r is the same) and the tension throughout the entire rope is the same (meaning F is the same), we know that the counterclockwise torque cancels out the clockwise torque, thus, the net torque is zero.
In the image below, T1 (due to the platform with the 4 0.5kg weights) = T2 (the 2kg mass).
Example Question #2 : Torque
Two students are balancing on a 10m seesaw. The seesaw is designed so that each side of the seesaw is 5m long. The student on the left weighs 60kg and is standing three meters away from the center. The student on the right weighs 45kg. The seesaw is parallel to the ground. Assume the board that makes the seesaw is massless.
What distance from the center should the student on the right be if they want the seesaw to stay parallel to the ground?
Torque is defined by the equation . Since both students will exert a downward force perpendicular to the length of the seesaw, . In our case, force is the force of gravity, given below, and is the distance from the center of the seesaw.
Since the torque must be zero in order for the seesaw to stay parallel (not move), the lighter student on the right must make his torque on the right equal to the torque of the student on the left. We can determine the required distance by setting their torques equal to each other.
Example Question #2 : Torque
Two students are balancing on a 10m seesaw. The seesaw is designed so that each side of the seesaw is 5m long. The student on the left weighs 60kg and is standing three meters away from the center. The student on the right weighs 45kg. The seesaw is parallel to the ground. Assume the board that makes the seesaw is massless.
Imagine that the two students are sitting on the seesaw so that the torque is . Which of the following changes will alter the torque of the seesaw?
The heavier student moves forward 1m, while the lighter student moves forward 1.33m.
Another student stands perfectly on the center of the seesaw.
Two more students get on the seesaw, each weighing 45kg. They both sit on opposite ends of the seesaw, five meters away from the center.
Both students move toward the center by one meter.
Both students move toward the center by one meter.
Torque, in this case, is dependent on both the force exerted by the students as well as their distances from the point of rotation. As a result, both students moving forward by one meter will cause a nonzero torque on the seesaw. This is because the heavier student's ratio of force and distance will result in less torque on his side than the lighter student.
Example Question #2 : Torque
A 3m beam of negligible weight is balancing in equilibrium with a fulcrum placed 1m from it's left end. If a force of 50N is applied on it's right end, how much force would needs to be applied to the left end?
This a an example of rotational equilibrium involving torque. The formula for torque is , where is the angle that the force vector makes with the object in equilibrium and is the distance from the fulcrum to the point of the force vector. To achieve equilibrium, our torques must be equal.
Since the forces are applied perpendicular to the beam, becomes 1. The distance of the fulcrum from the left end is 1m and its distance from the right end is 2m.
Since the 50N force is twice as far from the fulcrum as the force that must be applied on the left side, it must be half as strong as the force on the left. The force on the left can be found to be 100N.
Example Question #1 : Torque
One side of a seesaw carries a mass four meters from the fulcrum and a mass two meters from the fulcrum. To balance the seesaw, what mass should be placed nine meters from the fulcrum on the side opposite the first two masses?
For the seesaw to be balanced, the system must be in rotational equilibrium. For this to occur, the torque the same on both sides.
The total torque must be equal on both sides in order for the net torque to be zero.
Substitute the formula for torque into this equation.
Now we can use the given values to solve for the missing mass.
The acceleration form gravity cancels from each term.