Question

what is the relationship between linear and angular speed.​

Answer 1

V = r w

v is linear speed

w is angular speed

Proof M1 :

$\lim_{n \to \infty} a_n \lim_{n \to \infty} a_n \lim_{n \to \infty} a_n \lim_{n \to \infty} a_n \int\limits^a_b {x} \, dx \int\limits^a_b {x} \, dx \int\limits^a_b {x} \, dx \geq \geq \neq \sqrt[n]{x} \sqrt{x} x^{2} \alpha \alpha \alpha \sqrt{x} x^{2} x^{2} \geq \int\limits^a_b {x} \, dx \int\limits^a_b {x} \, dx \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left \{ {{y=2} \atop {x=2}} \right. \leq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \leq x^{2} \sqrt[n]{x} \frac{x}{y} \frac{x}{y} \frac{x}{y} x_{123} x_{123} x_{123} \beta \beta \alpha \alpha \alpha \pi \neq \neq \neq$Hence prooved

Proof M2 :

Assuming v=rw

hence prooved.

Answer 2

Answer:

Linear velocity

v

is equal to the angular speed

ω

times the radius from the center of motion

R

.

We can derive this relationship from the arclength equation

S

=

θ

R

where

θ

is measured in radians.

Start with

S

=

θ

R

Take a derivative with respect to time on both sides

d

S

dt

=

d

θ

dt

R

d

S

dt

is linear velocity and

d

θ

dt

is angular velocity

So we're left with:

v

=

ω

R

Explanation:

Relation between linear velocity and angular velocity

Let us consider a body P moving along the circumference of a circle of radius r with linear velocity v and angular velocity ω as shown in Fig.. Let it move from P to Q in time dt and dθ be the angle swept by the radius vector.

Let PQ = ds, be the arc length covered by the particle moving along the circle, then the angular displacement d θ is expressed as dθ = ds/r. But ds=vdt.

d θ/dt=v/r

(i.e) Angular velocity ω = v/r or v =ω r

In vector notation,

Vector v = Vector ω x Vector r

Thus, for a given angular velocity ω, the linear velocity v of the particle is directly proportional to the distance of the particle from the centre of the circular path (i.e) for a body in a uniform circular motion, the angular velocity is the same for all points in the body but linear velocity is different for different points of the body.