Homework help.....?

Question

A bunny on a 15cm string starts from rest and reaches 10rpm in 20s. Find:
(a) The angular velocity
(b) The final linear velocity
(c) The final centripedal acceleration
(d) The tangential acceleration...

i'm not asking for answers... i'm asking for a way to solve it.. first person with the best description gets 10 pts. GL

Answer 1

What are the units of angular velocity?....Radians per second. What are radians? Radians are used to measure angles. So really, annular velocity (as the name implies) measures how fast an object is moving "angularly" from a given point of rotation.
After completing one "cycle" around the circle an object moves 2*pi radians. Divide the angular distance traveled by the time it takes to move this distance.
You are given an RPM measurement telling just how many revolutions the bunny makes in a given minute, convert this to radians per second by multiplying 10 revolutions by 2*pi radians per revolution, then multiply by 60 seconds per minute to get radians per second.

Converting from angular measurements to linear measurements or vice versa is easy when you know the formula,
Angular velocity = linear velocity / radius
However it is also good to know the concept behind it.
If you were to "unroll" the circular path into a straight line how long would it be? (Use the circumference of the circle to do this). Relate how long it takes for the object to cover this linear distance with respect to time.

Using the formula,
a_c = v^2 / r
it is merely a matter of plugging in the numbers to find the centripetal acceleration. Here the "v" is the linear speed of the object and r is the radius of rotation.

The tangential acceleration can be related to the angular acceleration (a change on angular speed with respect to time) in a similar way to how angular velocity is related to linear velocity,
Angular acceleration = tangential acceleration / radius
You are given a time span in which the object's angular speed increased from zero to ___ (found in part "a"). To find the angular acceleration, divide the change in angular velocity by the change in time. Then use the angular acceleration to find the tangential acceleration.