Calculating Angular Velocity & Revolutions for a Merry-Go-Round

In summary, the merry-go-round is accelerated from rest at a steady rate of 0.2 rad.s-2 by a child. To find the time it takes for the merry-go-round to reach an angular velocity of 1.4 rad.s-1, the equation t=w/a can be used. To find the number of revolutions made in this time, the equation N=\frac{\theta}{2\pi} can be used, where \theta=\frac{1}{2}at^2. The equation w=\frac{\theta}{t} should not be used as it only gives an average angular frequency and does not take into account the acceleration.
  • #1
sauri
51
0
A merry-go-round is accelerated from rest by a child at a steady acceleration of 0.2 rad.s-2.

1)How long does it take for the merry go round to reach an angular velocity of 1.4 rad.s-1?
2)How many revolutions does the merry go round (and the child) make in this time?

I believe I worked out the first one, where a=w/t. so t=w/a (t=1.4/0.2). Am I correct?.

However I can't understand the second part..is there an equation to find the number of revs?
 
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  • #2
The first question, I think you're right.
For the second one, find the angle [itex]\theta=\frac{1}{2}at^2[/itex]
The revolutions are [itex]N=\frac{\theta}{2\pi}[/itex]
 
  • #3
is it ok to use w=[itex]\theta/t to find the angle?
 
  • #4
sauri said:
is it ok to use w=[itex]\theta/t to find the angle?

No because this will only give you an average angular frequencey. As there is acceleration you need to use the equations phuncv87 posted.
 

FAQ: Calculating Angular Velocity & Revolutions for a Merry-Go-Round

What is angular velocity?

Angular velocity is a measure of how quickly an object is rotating around a fixed axis. It is typically measured in radians per second.

How do you calculate angular velocity?

Angular velocity can be calculated by dividing the angular displacement (change in angle) by the time it takes to complete that rotation. It can also be calculated by dividing the linear velocity (speed) by the distance from the axis of rotation.

What is the formula for calculating angular velocity?

The formula for calculating angular velocity is ω = Δθ/Δt, where ω represents angular velocity, Δθ represents angular displacement, and Δt represents time.

What is the relationship between angular velocity and linear velocity?

Angular velocity and linear velocity are related through the distance from the axis of rotation. As the distance from the axis increases, linear velocity increases at a proportional rate to angular velocity.

How do you calculate the number of revolutions for a merry-go-round?

The number of revolutions for a merry-go-round can be calculated by dividing the total angular displacement (360 degrees or 2π radians) by the angular displacement per revolution. Alternatively, it can be calculated by dividing the total distance traveled by the circumference of the merry-go-round.

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