Circular Motion and Trigonometry

Questions and Answers

What do you multiply degrees by to convert an angle from degrees to radians?

pi/180

What is the formula involving ω to calculate the linear velocity of a particle in circular motion?

v = ω * r

What is the physical interpretation of the angular velocity in circular motion?

The rate of change of angle with respect to time

What is the unit of linear velocity in circular motion?

meter per second Signup and view all the answers

What is the physical quantity that describes the speed of a particle in a direction perpendicular to the radius at a given point in circular motion?

Linear velocity Signup and view all the answers

What is the SI unit of the time taken for one complete revolution, cycle, or oscillation of an object in circular motion?

Seconds (s) Signup and view all the answers

What is the angular quantity that is the rate of change of angle with respect to time in circular motion and what is its formula?

Angular velocity Signup and view all the answers

What is the direction of centripetal acceleration in an object moving in uniform circular motion?

Toward the centre of the circle Signup and view all the answers

What is the condition necessary for an object to be accelerating, even if its velocity is constant?

Changing direction Signup and view all the answers

What is the physical significance of centripetal force in uniform circular motion?

Centripetal force is the force required to maintain uniform circular motion, directing the object towards the center of the circle. Signup and view all the answers

How does the mass of an object affect its centripetal force in circular motion?

The centripetal force is directly proportional to the mass of the object, meaning that as the mass increases, the centripetal force required to maintain circular motion also increases. Signup and view all the answers

What determines the magnitude of centripetal force in circular motion?

The magnitude of centripetal force is determined by the square of the angular velocity, the mass of the object, and the radius of the circle. Signup and view all the answers

How does the radius of the circle affect the centripetal force required to maintain circular motion?

The centripetal force is inversely proportional to the radius of the circle, meaning that as the radius increases, the centripetal force required to maintain circular motion decreases. Signup and view all the answers

What is the relationship between centripetal force and acceleration in circular motion?

The centripetal force is the force that causes the centripetal acceleration, which is the acceleration that keeps an object moving in a circular path. Signup and view all the answers

What is the force that balances the centripetal force in an object moving in circular motion?

Centrifugal force Signup and view all the answers

What is the relationship between the periodic time of a satellite's orbit and the radius of the orbit, according to Kepler's third law?

The square of the periodic time is proportional to the cube of the radius of the orbit Signup and view all the answers

What is the periodic time of an orbit?

It is the time taken for a satellite to go once around the central body Signup and view all the answers

What is the symbol G that appears in Kepler's third law?

Universal constant of gravitation Signup and view all the answers

Study Notes

Converting between Degrees and Radians

To convert an angle from degrees to radians, multiply degrees by pi divided by 180.

Linear Velocity in Circular Motion

The formula to calculate the linear velocity of a particle in circular motion is v = ω multiplied by r.
The unit of linear velocity is meter per second.
Linear velocity is the physical quantity that describes the speed of a particle in a direction perpendicular to the radius at a given point in circular motion.

Angular Velocity in Circular Motion

The physical interpretation of the angular velocity is the rate of change of angle with respect to time.
The angular velocity is the rate of change of angle with respect to time in circular motion.

Time and Units in Circular Motion

The SI unit of the time taken for one complete revolution, cycle, or oscillation of an object in circular motion is seconds (s).

Centripetal Acceleration and Force

The direction of centripetal acceleration in an object moving in uniform circular motion is toward the centre of the circle.
The condition necessary for an object to be accelerating, even if its velocity is constant, is changing direction.
The physical significance of centripetal force in uniform circular motion is that it is the force required to maintain uniform circular motion, directing the object towards the center of the circle.
The centripetal force is directly proportional to the mass of the object.
The magnitude of centripetal force is determined by the square of the angular velocity, the mass of the object, and the radius of the circle.
The centripetal force is inversely proportional to the radius of the circle.
The centripetal force causes the centripetal acceleration, which is the acceleration that keeps an object moving in a circular path.
The force that balances the centripetal force in an object moving in circular motion is centrifugal force.

Kepler's Third Law

The square of the periodic time is proportional to the cube of the radius of the orbit.
The periodic time of an orbit is the time taken for a satellite to go once around the central body.
The symbol G that appears in Kepler's third law represents the universal constant of gravitation.

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Quiz on converting between degrees and radians, linear velocity in circular motion, and other concepts related to circular motion and trigonometry.