Angular displacement, velocity and acceleration

[wellz121]

I have a few problems that I am very confused on. If someone could walk me through them that would be a big help.

1. An antique spring-driven Victrola phonograph plays recordings at 78 rpm. At the end of each record the arm hits a lever that activates a brake that brings the record to rest in 1.3 s. Through how many radians does it turn in the process of stopping?

2. Placed on a long incline, a wheel is released from rest and rolls for 30.0 s until it reaches a speed of 11.0 rad/s. Assume its acceleration is constant, what angle did it turn through?

3. What is the average angular speed of the Earth in its orbit? Take a year to be 365.24 days. Give your answer to three significant figures.

 

[jdwood983]

Made a mistake on this one...see the post below instead

 

[jdwood983]

I think you're placing these in the wrong forum, these should be in the Introductory Physics...

I have a few problems that I am very confused on. If someone could walk me through them that would be a big help.

1. An antique spring-driven Victrola phonograph plays recordings at 78 rpm. At the end of each record the arm hits a lever that activates a brake that brings the record to rest in 1.3 s. Through how many radians does it turn in the process of stopping?

You have an angular velocity, \omega=78 rpm and a time t=1.3 s, so then either convert \omega into revolutions per second or t into minutes, multiply the two then convert from revolutions to radians.

2. Placed on a long incline, a wheel is released from rest and rolls for 30.0 s until it reaches a speed of 11.0 rad/s. Assume its acceleration is constant, what angle did it turn through?

You're given an initial and final angular velocity, \omega_i=0 and \omega_f=11 rad/s respectively. If you subtract the initial angular velocity from the final angular velocity, \omega_f-\omega_i and then divide by the time given, you will have the angular acceleration, \alpha. Using \alpha, \omega_i, t, you should put it into the rotational kinematic equation

<br /> \theta=\omega_it+\frac{1}{2}\alpha t^2<br />

then you can find the total angle through which it rotated in the motion.

3. What is the average angular speed of the Earth in its orbit? Take a year to be 365.24 days. Give your answer to three significant figures.

The Earth travels 2\pi radians per year. If you convert days into hours into minutes, you can divide the angle, 2\pi, by the time to get radians per minute. Then convert radians into revolutions so that you'll have revolutions per minute.