Angular acceleration, is my method correct?

[Dannystu]

Homework Statement

A Pulley has mass M=4 kg and radius R=0.4 m. Assume that it is a uniform solid disk so that its moment of inertia is I= .5MR^2. A massless cord is wrapped around it and a tension force Ft is applied. The pulley starts from rest. After the tension force has been applied for 6 seconds, the angular speed has reached T=60 rads/s.

Homework Equations

a.) What is the pulley's angular acceleration?

b.) What is the linear (tangential) acceleration of a point on the rim of the pulley?

The Attempt at a Solution

a.) V=(2*pi*R)/T
V= .418 m/s

w=v/r
w=1.045 rads/sec

angular acceleration= w2-w1/t2-t1
= (1.045-0)/(6-0)
= .15 rads/s^2

b.) Tangential acceleration= r*alpha
=.o2 m/s^2


Can anyone please tell me if this is correct?? Thank you thank you!

 

[LowlyPion]

Consider that it is uniform acceleration and

ω = a*t

a) is given simply by

60 = a*6 or a = 10 rad/sec²

b) would be determined by the same method you used.

 

[nlightner]

I would like to commend you on your attempt at solving this problem. However, there are a few things that need to be addressed in your solution.

Firstly, in part a), your calculation for the initial angular velocity (w1) is incorrect. It should be w1 = 0, as the pulley starts from rest. Also, your calculation for the final angular velocity (w2) is incorrect. It should be w2 = 60 rads/s, as given in the problem statement. Therefore, the correct calculation for angular acceleration would be (60-0)/(6-0) = 10 rads/s^2.

Secondly, in part b), your calculation for tangential acceleration is incorrect. It should be a = r*alpha = (0.4 m)*(10 rads/s^2) = 4 m/s^2.

Lastly, it is important to always include units in your calculations to ensure accuracy. In this case, the units for angular acceleration would be rads/s^2 and for tangential acceleration would be m/s^2.

In conclusion, your method is not entirely correct, but with a few adjustments, you will arrive at the correct answers. Keep up the good work!