How Can Circular Motion Principles Solve Real-World Physics Problems?

[hshphyss]

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

 

[lightgrav]

1) is not quite right ... 5.5 (2 pi) [rad] /1.2 is the average angular speed,
not the final angular speed. (why convert [1/s] to [1/min] to [1/s] ?)

2) if you convert 16 pi [rad/s] into 8 [rev/s], you might realize how far it travels in 5 seconds. Don't forget that the average speed was 4 [rev/s]

 

[quicknote]

.

For problem 1, your calculations are correct. The angular acceleration of the wheel can be found by using the formula a = (vf - vi)/t, where vf is the final angular velocity, vi is the initial angular velocity (which is 0 in this case), and t is the time. So, the angular acceleration would be (28.8 rad/s - 0 rad/s)/1.2 s = 24 rad/s^2.

For problem 2, you can use the formula vf = vi + at to find the angular acceleration. In this case, vf is 0 rad/s (since the tub comes to rest), vi is 50.3 rad/s (converted from 16pi rad/s), and t is 14.0 s. So, the angular acceleration would be -3.59 rad/s^2 (negative sign indicates deceleration). To find the number of revolutions, you can use the formula θ = vi*t + (1/2)*a*t^2, where θ is the angular displacement, vi is the initial angular velocity, a is the angular acceleration, and t is the time. In this case, θ would be the number of revolutions, vi is 50.3 rad/s, a is -3.59 rad/s^2, and t is 14.0 s. Plugging in the values, you would get θ = 280.8 revolutions.

For problem 3, the formula for centripetal acceleration is a = 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 linear velocity of Earth's rotation, which is approximately 1670 km/h (463.9 m/s). The radius of the Earth at the equator is approximately 6378 km (6,378,000 m). Plugging in the values, you would get a = (463.9 m/s)^2 / 6,378,000 m = 0.034 m/s^2. At the North Pole, the tangential velocity is 0, so the centripetal acceleration would also be 0.