2 Views

what is the velocity at the top most point when a object is moving in a ciircular path


Sumit sharma 11th Sep, 2024
Answer (1)
monag2673 12th Sep, 2024

When an object is moving in a circular path, the velocity at the topmost point of the path can be analyzed in the context of uniform circular motion. Here's a breakdown:


1. **Definition of Velocity in Circular Motion**: Velocity in circular motion is always tangential to the path. This means the speed is constant if the motion is uniform, but the direction of velocity changes continuously.


2. **Topmost Point in Circular Motion**: At the topmost point of a vertical circular path, gravity acts downward while the centripetal force needed to keep the object in circular motion also acts downward. The net force acting on the object provides the centripetal force required for circular motion.


3. **Expression for Velocity**: The centripetal force \(F_c\) required to keep the object moving in a circle of radius \(r\) with velocity \(v\) is given by:

\[

F_c = \frac{mv^2}{r}

\]

At the topmost point, the gravitational force \(mg\) helps provide the centripetal force, so:

\[

mg + N = \frac{mv^2}{r}

\]

where \(N\) is the normal force at the topmost point. For an object just moving in the circle (minimal normal force), \(N\) can be approximated as zero:

\[

mg = \frac{mv^2}{r}

\]

Solving for \(v\):

\[

v = \sqrt{gr}

\]


In summary, at the topmost point of a vertical circular path, the velocity \(v\) can be found using \(v = \sqrt{gr}\), where \(g\) is the acceleration due to gravity and \(r\) is the radius of the circle.

Related Questions

UPES Integrated LLB Admission...
Apply
Ranked #28 amongst Institutions in India by NIRF | Ranked #1 in India for Academic Reputation by QS University Rankings | 16.6 LPA Highest CTC
SLAT 2025 - The Symbiosis Law...
Apply
Conducted by Symbiosis International (Deemed University) | Ranked #5 in Law by NIRF | Ranked #2 among best Pvt Universities by QS World Rankings
Jindal Global Law School Admi...
Apply
Ranked #1 Law School in India & South Asia by QS- World University Rankings | Merit cum means scholarships
Symbiosis Law School Pune Adm...
Apply
NAAC A++ Accredited | Ranked #5 by NIRF
Nirma University Law Admissio...
Apply
Grade 'A+' accredited by NAAC
ISBR Business School PGDM Adm...
Apply
Ranked as Platinum Institute by AICTE for 5 years in a row | Awarded Best Business School of the Year
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books