Angular acceleration and angular velocity

In summary, the child on the merry-go-round is sitting on a horse onto a stationary pole 10m from the center of the merry-go-round. The ride starts from rest and with constant angular accleration obtains an angular velocity of 2 rad/s in 10 seconds. It then continues at 2 rad/s for 15 seconds and then brakes and comes to a stop with a deceleration of -0.1 rad/s^2.
  • #1
heyrefusuck
4
0
A child riding a merry-go-round is sitting on a horse onto a stationary pole 10m from the center of the merry-go-round. The ride starts from rest and with constant angular accleration obtains an angular velocity of 2 rad/s in 10 seconds. It then continues at 2 rad/s for 15 seconds and then brakes and comes to a stop with a deceleration of -0.1 rad/s^2.
1. Graph the angular velocity from start to stop
2. At 20 seconds, what is the centripital accleration of the child on the merry go round?
3. At 30 seconds, what is the tangential accelration of the child on the merry go round?
4. At 5 seconds, what is the magnitude of the total accel. of the child on the merry go round
5. What is the total angle, theta, that the merry go round travels during the first 15 seconds?

thank you in advance!
 
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  • #2
Welcome to PF.

What are your thoughts on how to approach it?
 
  • #3
Well, in response to #2 I would use the following formula: centripetal accel. = v^2/r but what would be the unit? rad/sec/m? Accel. unit needs a distance unit and two units of time correct?
So would it be 2 rad/s squared divided by the radius (10)?
#3 I would use tangential accel. = a(tangential accel.) = accel. x radius Will this be in m/s^2?
As far as the graph (#1) goes I’m not sure and would certainly entertain ideas on how to attack #4 and #5. Thx…
 
  • #4
heyrefusuck said:
Well, in response to #2 I would use the following formula: centripetal accel. = v^2/r but what would be the unit? rad/sec/m? Accel. unit needs a distance unit and two units of time correct?
So would it be 2 rad/s squared divided by the radius (10)?
#3 I would use tangential accel. = a(tangential accel.) = accel. x radius Will this be in m/s^2?
As far as the graph (#1) goes I’m not sure and would certainly entertain ideas on how to attack #4 and #5. Thx…

First of all maybe you want to draw the graph for 1) by determining the radial acceleration over the first 10 sec.

You could use v2/r to yield centripetal acceleration, but ω = v/r maybe there is an easier formula that yields the same result like ω2*r ?

For 4) they want the components of acceleration. Since tangential acceleration is a vector and centripetal acceleration is a vector, simply add them like vectors using ordinary means.

For 5) just figure the area under your graph, since the integral of ω will yield total θ .
 

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 different from linear acceleration?

Angular acceleration is a measure of how quickly an object's rotational speed is changing, while linear acceleration is a measure of how quickly an object's linear velocity is changing. Angular acceleration is measured in radians per second squared, while linear acceleration is measured in meters per second squared.

3. What is the relationship between angular velocity and angular acceleration?

Angular velocity is the rate of change of an object's angular position over time, while angular acceleration is the rate of change of angular velocity over time. In other words, angular velocity is the first derivative of angular position, and angular acceleration is the second derivative of angular position.

4. How is angular velocity represented mathematically?

Angular velocity is typically represented by the Greek letter "omega" (ω). It is equal to the change in angular position (θ) over time (t), or ω = Δθ/Δt.

5. How can angular velocity and angular acceleration be measured?

Angular velocity and angular acceleration can be measured using specialized instruments such as accelerometers, gyroscopes, and tachometers. These instruments can provide precise measurements of an object's rotational speed and changes in rotational speed over time.

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