Circular Motion and Centripetal Force

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Questions and Answers

What is the frequency of revolution of the merry-go-round in the given scenario?

$\frac{\pi}{3}$ rev/s (correct)

$\frac{2\pi}{3}$ rev/s

$\frac{5\pi}{3}$ rev/s

$\frac{4\pi}{3}$ rev/s

In a controlled vertical circular motion, what primarily governs the speed?

Gravity

Tension in the rod

Inertia

Initial energy input (correct)

What is the radius of the horizontal circular motion of the rider on the merry-go-round?

1.5 m

2.1 m

3.0 m (correct)

3.6 m

What happens to the linear speed of a marble in a funnel as it approaches the brim?

It increases Signup and view all the answers

Which force is responsible for governing a vertical circular motion controlled only by gravity?

Gravitational force Signup and view all the answers

What is the interconversion process observed during the motion in a vertical circular motion controlled only by gravity?

Interconversion of kinetic and potential energy Signup and view all the answers

What is the role of the centrifugal force in explaining the feeling of being at rest on a merry-go-round?

Equal in magnitude to the resultant real force and directed opposite Signup and view all the answers

How does tangential velocity relate to circular motion?

Matching tangential velocity is essential for circular motion Signup and view all the answers

What is the nature of centrifugal force in a rotating frame of reference?

Arises due to centripetal acceleration Signup and view all the answers

Why does a spring balance read more mass when whirling a mass in horizontal circular motion?

Centrifugal force adds to the actual weight of the mass Signup and view all the answers

Which force is responsible for keeping a car on a horizontal circular track?

Centripetal force pulling inward Signup and view all the answers

In which reference frame is it necessary to consider centrifugal force?

In a frame rotating with uniform speed Signup and view all the answers

What is the main difference between revolution and rotation?

Revolution involves circular motion about a point outside the object, while rotation involves motion about an axis passing through the object. Signup and view all the answers

What characteristic defines circular motion as accelerated?

The direction of velocity changes at every instant. Signup and view all the answers

What term describes the motion where the particle repeats its path along the same trajectory?

Periodic motion Signup and view all the answers

What quantity is analogous to displacement in translational motion for describing circular motion?

Angular displacement Signup and view all the answers

How is tangential velocity related to angular velocity in circular motion?

$v = r / ω$ Signup and view all the answers

How is the direction of angular velocity determined in circular motion?

By using the fingers to curl according to a rule Signup and view all the answers

Study Notes

Characteristics of Circular Motion

Circular motion is an accelerated motion since the direction of velocity changes at every instant.
Circular motion is a periodic motion as the particle repeats its path along the same trajectory.

Kinematics of Circular Motion

Angular displacement (θ), angular velocity (ω), and angular acceleration (α) are used to describe circular motion.
These quantities are analogous to displacement (s), velocity (v), and acceleration (a) used in translational motion.
Tangential velocity (v) is given by v = ωr, where ω is the angular velocity and r is the radius vector from the centre of the circular motion.

Centripetal Force and Centrifugal Force

Centripetal force (mv^2/r) is essential for circular motion to occur.
Centrifugal force (mv^2/r) is a pseudo force that arises due to the centripetal acceleration of the frame of reference.
Centrifugal force is directed away from the centre and is equal in magnitude to the resultant real force.

Applications of Uniform Circular Motion

A car moving along a horizontal circular track of radius r is an example of uniform circular motion.

Vertical Circular Motion

There are two types of vertical circular motions: controlled vertical circular motion (e.g., a giant wheel) and vertical circular motion controlled only by gravity (e.g., a projectile motion).
In controlled vertical circular motion, the speed is either kept constant or not totally controlled by gravity.
In vertical circular motion controlled only by gravity, the kinetic energy and gravitational potential energy are interconverted during the motion.

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Description

This quiz discusses the concept of circular motion, tangential velocity, centripetal force, and centrifugal force in an inertial frame of reference. It explains how the body moves in a circular path and the forces involved in maintaining the motion.