Question

plzz help itz imp!!!!!​

Answer 1

Answer:

.

Explanation:

Radian measure and arc length can be applied to the study of circular motion. In physics the average speed of an object is defined as:

average speed=distance traveledtime elapsed

So suppose that an object moves along a circle of radius r, traveling a distance s over a period of time t, as in Figure 1. Then it makes sense to define the (average) linear speed ν of the object as:

v=st(1)

Let θ be the angle swept out by the object in that period of time. Then we define the (average) angular speed ω of the object as:

ω=θt(2)

Angular speed gives the rate at which the central angle swept out by the object changes as the object moves around the circle, and it is thus measured in radians per unit time. Linear speed is measured in distance units per unit time (e.g. feet per second). The word linear is used because straightening out the arc traveled by the object along the circle results in a line of the same length, so that the usual definition of speed as distance over time can be used. We will usually omit the word average when discussing linear and angular speed here.

Since the length s of the arc cut off by a central angle θ in a circle of radius r is s = r θ, we see that

v=st=rθt=θt.r

so that we get the following relation between linear and angular speed:

v=ωr(3)

Answer 2

Answer:

What is the relationship between linear speed and angular speed?

Physics Displacement and Velocity

1 Answer

Peter A.

Jul 17, 2015

v

=

ω

R

Explanation:

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

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