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Level 88

Circular & Rotational Motion


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When it's moving in a circle at *constant speed*.
When is an object moving in *uniform circular motion* (UCM)?
centripetal acceleration
a = centripetal acceleration
What is centripetal force?
The *net* force (sum of the forces) that causes an object to move in a circle (uniform circular motion).
Centripetal Force
A force directed towards the center of a circle that causes an object to follow a circular path
Relative to the center of the circle. The convention is:
In uniform circular motion, how do you indicate direction (positive & negative directions)?
At any point on a uniform circular motion path, what is the direction of *velocity*?
Tangent to the circle, in the direction the object would move if it left the circle.
Towards the center of the circle.
At any point on a uniform circular motion path, what is the direction of *centripetal acceleration*?
What is a period in uniform circular motion?
The time it takes for an object to complete one revolution (one circumference).
What is frequency in uniform circular motion?
The number of revolutions an object makes per unit of time.
They're reciprocals of each other.
How are period and frequency related to each other?
Speed
Units: cm/s, m/s, mi/hr, km/s ...
Short answer: inertia.
In UCM, if the net force (centripetal force) is pulling the object towards the center, why doesn't the object fall into the center instead of continuing to travel in a circle?
What is torque?
The result of a force acting at a distance from an axis of rotation.
Torque
A "force" that causes rotation because it is exerted at a distance from the axis of rotation.
When will torque cause an object to rotate?
When the force has a component that is perpendicular to the radius of rotation.
By direction of rotation.
How are the directions of torque assigned?
angular momentum
analogous to momentum; if the net torque on a system is zero then the angular momentum is conserved
What is the difference between *linear momentum* and *angular momentum*?
Angular momentum applies to objects that move in curved paths (like a circle).
When is angular momentum conserved?
When there is no net torque.
When is there rotational equilibrium?
When there is no net torque.
Decrease.
How will a lighter mass affect the period of a spring?
Increase.
How will a heavier mass affect the period of a spring?
Larger mass should be placed closer to the axis of rotation.
If a smaller mass is placed some distance away from the axis of rotation, where must a larger mass be placed on the lever so that the net torque equals zero (the lever doesn't rotate)?
Smaller mass should be placed farther from the axis of rotation.
If a larger mass is placed some distance away from the axis of rotation, where must a smaller mass be placed on the lever so that the net torque equals zero (the lever doesn't rotate)?