Give an example in which there are clear distinctions among distance traveled, displacement, and magnitude of displacement. spec
ifically identify each quantity in your example.
1 answer:
The example I've given is shown as an illustration in the picture. Suppose a jogger covers 2 km as he heads to the east. Then, he heads up north for another 1.5 km. Now, if you are to find the distance, you simply have to take the sum.
Distance = 2 + 1.5 = 3.5 km
If you are to find the displacement, you find the distance from the starting point to the end point, represented by the red arrow. Using the pythagorean theorem,
Displacement = √(2 km)² + (1.5 km)² = 2.5 km
If you are to find the magnitude of displacement, this is equivalent to distance. So, it is equal to 3.5 km. The displacement is a vector quantity, which presents the magnitude and the direction. The magnitude of the displacement does not take into account the direction of motion, just the total distance covered.
Distance = 2 + 1.5 = 3.5 km
If you are to find the displacement, you find the distance from the starting point to the end point, represented by the red arrow. Using the pythagorean theorem,
Displacement = √(2 km)² + (1.5 km)² = 2.5 km
If you are to find the magnitude of displacement, this is equivalent to distance. So, it is equal to 3.5 km. The displacement is a vector quantity, which presents the magnitude and the direction. The magnitude of the displacement does not take into account the direction of motion, just the total distance covered.
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Torque can cause the angular momentum vector to rotate in UCM. This motion is called _Conservation of Angular momentum__________.
Answer:
Conservation of Angular momentum
Explanation:
The motion of an object in a circular path at constant speed is known as uniform circular motion (UCM). An object in UCM is constantly changing direction, and since velocity is a vector and has direction, you could say that an object undergoing UCM has a constantly changing velocity, even if its speed remains constant.
The law of conservation of angular momentum states that when no external torque acts on an object, no change of angular momentum will occur.
Key Points
When an object is spinning in a closed system and no external torques are applied to it, it will have no change in angular momentum.
The conservation of angular momentum explains the angular acceleration of an ice skater as she brings her arms and legs close to the vertical axis of rotation.
If the net torque is zero, then angular momentum is constant or conserved.
Angular Momentum
The conserved quantity we are investigating is called angular momentum. The symbol for angular momentum is the letter L. Just as linear momentum is conserved when there is no net external forces, angular momentum is constant or conserved when the net torque is zero. We can see this by considering Newton’s 2nd law for rotational motion:
τ→=dL→dt, where
τ is the torque. For the situation in which the net torque is zero,
dL→dt=0.
If the change in angular momentum ΔL is zero, then the angular momentum is constant; therefore,
⇒
L =constant
L=constant (when net τ=0).
This is an expression for the law of conservation of angular momentum.
Example and Implications
An example of conservation of angular momentum is seen in an ice skater executing a spin, The net torque on her is very close to zero,
because (1) there is relatively little friction between her skates and the ice, and (2) the friction is exerted very close to the pivot point.
Conservation of angular momentum is one of the key conservation laws in physics, along with the conservation laws for energy and (linear) momentum. These laws are applicable even in microscopic domains where quantum mechanics governs; they exist due to inherent symmetries present in nature.
