Velocity - Definition, Example, Types, FAQs

Hello

I hope you are absolutely fine. As per your mentioned query, speed is a scalar quantity which tells you how the object is moving fast. Whereas velocity is a vector quantity which tells you about the speed as well as direction.

I hope this helps you!

Revert for further query!

Hii,

If two objects are attached at the ends of a rigid body (like a rod or wheel), yes, their angular velocity remains the same.

Here's why:

• Angular velocity refers to how fast something is rotating (angle per unit time), not how fast it's moving in a straight line.

• In a rigid body, all points rotate with the same angular velocity around the axis of rotation.

• Even if the two objects are at different distances from the axis, their linear (tangential) velocities will be different, but their angular velocities will be the same.

Example:

Imagine two balls attached to the ends of a rotating stick:

• The stick rotates about its center.

• Both balls complete one full circle in the same amount of time.

• So, both have the same angular velocity (say, 2π radians per second).

• But the ball farther from the center travels a longer path in the same time → it has a higher linear speed, not angular speed.

To find the value of h, we need to use the concept of conservation of energy. At the lowest point, the bob has kinetic energy due to its velocity. As it rises, this kinetic energy is converted into potential energy.

Initial kinetic energy (KE) = (1/2)mv^2, where m is the mass of the bob and v is its velocity.

At the highest point, the bob has potential energy (PE) = mgh, where g is the acceleration due to gravity and h is the height above the center of the circle.

Since energy is conserved, KE = PE:

(1/2)mv^2 = mgh

Given:

- v = 7 m/s

- g = 9.8 m/s^2 (approximately)

Now, we can solve for h:

h = (1/2)v^2 / g

= (1/2)(7)^2 / 9.8

= 2.5 m

However, this is the total height from the lowest point. Since the length of the pendulum is 1m, the height above the center of the circle (h) would be:

h = 2.5 - 1

= 1.5 m

So, the value of h is approximately 1.5 meters.

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.

Hello,

The slope of the tangent drawn on a velocity-time graph at a particular instant of time is equal to the instantaneous acceleration at that time. This is because the slope of the tangent line represents the rate of change of velocity with respect to time, which is the definition of acceleration.

Hope this helps,

Thank you