Angular acceleration, displacement

• glasshut137
In summary, the flea lands at point B on the horizontal turntable 9.3 cm from the center and its linear speed is .33 m/s. Its angle relative to the fixed coordinate system is 41 degrees and the distance from point A to point B is 6.6 cm.
glasshut137
[SOLVED] angular acceleration, displacement

Homework Statement

A flea is at point A on a horizontal turntable 9.3 cm from the center. Place the coordinate origin at the center of the turntable withthe positive x-axis fixed in space and initially passing through A. THe turntable is rotating at 34 rev/min in the counterclockwise direction relative to the fixed coordinate system. Then the flea jumps upward (meaning that it adds only its own vertical velocity when it jumps, not to its horizontal velocity) to a height of 4.9 cm in the fixed coordinate system and lands on the turntable at point B. The acceleration of gravity is 9.8 m/s^2.
1) Find the linear displacement of the flea in the fixed coordinate system.

2) Find the angle relative to the fixed coordinate system through which point A has rotated when the flea lands.

3) Find the distance of point B from the origin in the fixed coordinate system when the flea lands.

4) What angle does the radius drawn through B make with the fixed x-axis when the flea lands.

5) what is the linear speed of the flea relative to the fixed coordinate system after it lands

The Attempt at a Solution

im not really sure how to look at this particular problem and set of questions. I'm not sure how to solve these types of questions.

Work out where the fly lands in the fixed coordinate system and the time it takes to do that. Use the initial velocity of the flea and g=9.8m/sec^2. Then post your work and if you are making mistakes I'm sure people will jump in and help. But you have to start.

ok so i tried finding the linear displacement relative to the origin by using the pythagorean theorem. d=sqrt(.049^2+.093^2)=.105m

is this correct for the first part of the question?

I'm afraid not. The flea has an initial velocity along the direction of rotation which is equal to it's linear speed on the turntable when it jumps. Find that. Next find how much time elapses for the flea's motion in the vertical direction. How much time elapses for the flea's vertical motion. It jumps up to 4.9cm and then falls back. Use thing like (1/2)gt^2. During that time how far did it's linear speed take it? Use things like v0*t. It will land (in the fixed coordinate system) the distance it would travel in the hopping time along it's initial linear direction of motion in the hopping time. This is just splitting the motion into components.

ok so i converted 34rev/min into m/s and got .33m/s which should be it's rotational velocity. So in order for me to find the displacement around this turntable i need to know how long the flea was in the air and use that to find the distance the table turned. I found the time by plugging it into y=(at^2)/2 and got .1 sec. That should be the time up so i multiplied by 2 to find the total time. Then i just used v=d/t to find the distance and got 6.6cm.

Now for the angle, would i just use arctan(theta)=the displacement found in A/ the radius?

ok actually i used s=r(theta) (using s as the displacement in A) and got theta=41degrees and it was right. Thanks a lot. Still trying to work through the last 3 parts.

Looks good so far. A is the original point that the flea jumped from. It's new angle in the fixed coordinate system is just the rotational velocity multiplied by the time the flea was in the air 0.2sec, right?

yeah i understand that now.

so for part three wouldn't the distance of point B from the origin just be the radius since the flea would land in the same spot relative to the the origin?

No. The point A moves in a circle around the origin in the fixed coordinate system. The track of the flea (discounting it's vertical motion) moves on a tangent to the circle. Point B will lie 6.6cm from ORIGINAL position of A and along this tangent. The radius of B will be larger than the radius of A.

ok i see what you mean.

so to find the distance i just used pythagorean to find the radius. For the next part i just used the the arctan(distance of y/distance of x). Would the linear speed of the flea be same as the rotational velocity given since that's the velocity at which it jumped?

Yes.

well i tried .33m/s as my asnwer and it was incorrect. I'm not sure what other linear speed the question could be referring to.

I guess they are thinking that after it lands, it returns to uniform rotational motion at the new radius?

ok i found the new linear speed using the new radius. Thanks a lot for all your help on this very long problem.

Very welcome, you are.

1. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity over time. It is a measure of how quickly an object's rotational speed is changing.

2. How is angular acceleration calculated?

Angular acceleration is calculated by taking the change in angular velocity and dividing it by the change in time. This can be represented by the equation α = Δω/Δt, where α is angular acceleration, Δω is the change in angular velocity, and Δt is the change in time.

3. What units is angular acceleration measured in?

Angular acceleration is typically measured in radians per second squared (rad/s^2) or degrees per second squared (deg/s^2), depending on the unit of measurement for angular velocity.

4. How is angular displacement different from linear displacement?

Angular displacement is a measure of the change in an object's rotational position, while linear displacement is a measure of the change in an object's linear position. Angular displacement is measured in radians or degrees, while linear displacement is measured in meters or feet.

5. Can an object have both angular and linear displacement?

Yes, an object can have both angular and linear displacement. For example, a wheel rolling along the ground has both angular displacement (as it rotates) and linear displacement (as it moves forward). However, the two displacements are independent of each other and are measured in different units.

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