Circular Motion Help! | Physics Questions Answered

[hshphyss]

Circular Motion Help!

Can anyone help me with these problems?

1.A tire placed on a balancing machine in a service station starts from rest and turns through 5.5 revs in 1.2 s before reaching its final angular speed. Assuming that the angular acceleration of the wheel is constant, calculate the wheel's angular acceleration.

--- I know you have to chance rev per s into revs per min into rad per s. So i did 5.5/(1.2/60)=275 rpm x (2pi/60)=28.8 rad/s. Is that right?
After I got that i used the formula vf=vi+at so 28.8=0+1.2. My time might be wrong but I was sure what to do.

2. The tub within a washer goes into its spin cycle, starting from rest and reaching an angular speed of 16pi rad/s in 5.0 s. At this point, the lid is opened, and a safety switch turns off the washer. The tub slows to rest in 14.0 s. Through how many revolutions does the tub turn? Assume constant angular acceleration while the machine is starting and stopping.

I chanced 16pi into 50.3 rad/s, and converted that to 480 rpms. The next part is where I get stuck. How would I set up the constant angular acceleration problem to help me get the revelutions. I know how to find the acceleration, but what would I do next?


3. (a)Find the centripetal accelerations of a point on the equator of Earth.
(b) Find the centripetal accelerations of a point at the North Pole of Earth.

 

[kp]

1) i no expert but, i think your using the wrong equation for this problem, your given a distance (5.5 revolutions in 1.2s) I would think that an equation that uses distance & time to find acceleration would be better, also you might check your conversions to rads again.

2) your given final angular speed and time, use a equation to find acceleration, then find distance distance (or revolutions). then convert to rpms.

 

[quicknote]

For problem 1, your calculations are correct. You have correctly converted the revolutions per second into radians per second and used the formula for final velocity to solve for angular acceleration. However, your units for time are incorrect. The time should be in seconds, not minutes. So the correct calculation would be 28.8 = 0 + (1.2/60)a, where a is the angular acceleration. This gives an angular acceleration of 24 radians per second squared.

For problem 2, you are on the right track. To find the number of revolutions, you need to use the formula for rotational motion, theta = theta0 + omega0t + 1/2at^2, where theta is the final angle, theta0 is the initial angle, omega0 is the initial angular velocity, t is the time, and a is the angular acceleration. In this case, theta is 2pi, theta0 is 0, omega0 is 50.3 radians per second, t is 14 seconds, and a is the angular acceleration you calculated in problem 1. Solve for theta and you will get the number of revolutions.

For problem 3, you can use the formula for centripetal acceleration, ac = v^2/r, where v is the tangential velocity and r is the radius of the circular motion. At the equator, the tangential velocity is equal to the speed of Earth's rotation, which is approximately 1670 kilometers per hour. You will need to convert this to meters per second and then divide by the radius of Earth (6371 kilometers) to get the centripetal acceleration. At the North Pole, the tangential velocity is zero, so the centripetal acceleration is also zero.