Angular acceleration and speed

[Knfoster]

Homework Statement

A mass attached to a 43.9 cm long string starts from rest and is rotated 35 times in 57.0 s before reaching a final angular speed. Determine the angular acceleration of the mass, assuming that it is constant and determine the angular speed after 57 sec.

Homework Equations

V=rW
W=2pi*f
f=1/T
T=time it takes for one revolution
3. The Attempt at a Solution
T=35/57 sec gives you T=.614 s
I'm not sure where to go from there... am I missing an equation that links all of these together?

 

[LowlyPion]

Consider these analogs to linear kinematics:
http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#rlin

As long as you keep things in radians, and radians/sec etc, you are in good shape.

 

[nlightner]

There are a few equations that can help us solve this problem:

1. Angular velocity (W) is equal to the change in angular displacement (theta) over the change in time (t). This can be written as W = (theta2 - theta1)/(t2 - t1). In this case, theta1 = 0, theta2 = 35 revolutions (since the mass starts from rest and rotates 35 times), and t1 = 0 s, t2 = 57 s. So, W = (35 rev)/(57 s) = 0.614 rev/s.

2. Angular acceleration (alpha) is equal to the change in angular velocity over the change in time. This can be written as alpha = (W2 - W1)/(t2 - t1). In this case, W1 = 0 rev/s (since the mass starts from rest), W2 = 0.614 rev/s (from the previous equation), t1 = 0 s, and t2 = 57 s. So, alpha = (0.614 rev/s - 0 rev/s)/(57 s) = 0.0108 rev/s^2.

3. We can also use the equation W = 2pi*f (where f is the frequency of rotation) to find the angular velocity. Since we know that the mass rotates 35 times in 57 seconds, the frequency is 35 revolutions/57 seconds = 0.614 rev/s. Plugging this into the equation, we get W = 2pi*(0.614 rev/s) = 1.93 rad/s.

So, the angular acceleration is 0.0108 rev/s^2 and the final angular speed after 57 seconds is 1.93 rad/s.