Calculating Angular and Linear Speed and period of revolution

In summary, a toy truck moves around a circle with a radius of 0.6m at a speed of 2 revolutions per second. To find the angular speed, we use ω=2π/T, where T is the period of revolution. The correct value is 12.56 radians/s. To find the linear speed, we use v=rω, where r is the radius and ω is the angular speed. The correct value is 7.54 m/s. The period of revolution is the time it takes for one revolution to occur, and in this case, it is 0.5 seconds.

Homework Statement

A toy truck moves around the outside of a circle of radius 0.6m at 2 revolutions per second

Calculate:
a: the angular speed of the truck
b: the linear speed of the truck
c: the period of revolution

Homework Equations

$ω= \frac{2π}{T} \\ v=rω$
??

The Attempt at a Solution

For part a i have done..
$ω= \frac{2π}{T} \\ ω= \frac{2π}{0.5} \\ ω= 12.56 rads/s$

I used 0.5 as it says it rotates twice per second so one rotation would take half a second (i think this maybe wrong).

For part b i have done..
$v=rω \\ v=0.6 \times 12.56 \\ v= 7.54m/s \\$
Obviously this depends on whether I got part a correct.

For part c I am not sure what the question is asking for but at a guess I did what I did in part A..

2 revolutions per second, therefore 1 revolution would take 0.5s.

Any help is appreciated.

Last edited:
What is 2 divided by .5? Last time I checked it was 4.

LawrenceC said:
What is 2 divided by .5? Last time I checked it was 4.

I understand that, but where does that relate to my answers? Have I divided 2 by 0.5 anywhere?

I do usually miss obvious things, and I can't see this one, could you point it out please?

EDIT: sorry I just released this mistake (i think) and rectified it.

I am not a native English speaker but I think it means the time one rotation takes. So for c T=0.5s

Could anyone have another look please and see if there is anything wrong with it now? Any help is appreciated :)

It is correct. Angular speed is 4*pi; linear speed is 2.4*pi; period is 0.5 seconds.

1. What is angular speed?

Angular speed, also known as angular velocity, is a measure of how quickly an object rotates about a fixed axis. It is typically measured in radians per second (rad/s) or degrees per second (deg/s).

2. How is angular speed calculated?

Angular speed can be calculated by dividing the angle traveled by the time it takes to travel that distance. The formula for angular speed is ω = θ / t, where ω is the angular speed in radians per second, θ is the angle traveled in radians, and t is the time it takes to travel that distance in seconds.

3. What is linear speed?

Linear speed, also known as tangential speed, is a measure of how quickly an object moves along a circular path. It is typically measured in meters per second (m/s) or feet per second (ft/s).

4. How is linear speed calculated?

Linear speed can be calculated by multiplying the angular speed by the radius of the circular path. The formula for linear speed is v = ω * r, where v is the linear speed in meters per second, ω is the angular speed in radians per second, and r is the radius of the circular path in meters.

5. What is the period of revolution?

The period of revolution, also known as the rotational period, is the time it takes for an object to complete one full revolution around a fixed axis. It is typically measured in seconds (s).

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