# Angular acceleration and angular velocity

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?

## The Attempt at a Solution

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LowlyPion
Homework Helper
Welcome to PF.

What are your thoughts on how to approach it?

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…

LowlyPion
Homework Helper
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 .