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

$$\theta=\omega_it+\frac{1}{2}\alpha t^2$$

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.