How Do You Calculate Angular Acceleration and Revolutions of a Stopping Wheel?

[badula]

Homework Statement

A wheel is spinning at 800 rad/s. A torque is applied to the wheel until it stops spinning 14 seconds later. What is the angular acceleration, and how many revolutions did it go through?

v=800 read/s
t=14 s

Homework Equations

angular acceleration = delta w / delta t
1 revolution = 360 degrees = 2 pi rad

The Attempt at a Solution

delta w/delta t = 800/14 = 57.1 rads/s²

57.1 / 2 pi = 9.09 revolutions

 

[tiny-tim]

Welcome to PF!

Hi badula ! Welcome to PF!

(have a pi: π and a delta: ∆ and an omega: ω )

A wheel is spinning at 800 rad/s. A torque is applied to the wheel until it stops spinning 14 seconds later. What is the angular acceleration, and how many revolutions did it go through?

Hint: you can use the usual linear equations of motion for uniform acceleration …

it's just like a linear speed of 800 m/s, stopping after 14 s, but with rad instead of m.

 

[thomate1]

The angular acceleration of the wheel is 57.1 rads/s2 and it went through 9.09 revolutions before coming to a stop. This can also be calculated by dividing the final angular velocity (0 rad/s) by the initial angular velocity (800 rad/s) and then multiplying by the time (14 s), which gives the same result of 9.09 revolutions. It is important to note that the angular acceleration is dependent on the torque applied to the wheel, as well as the moment of inertia of the wheel. The moment of inertia is a measure of how difficult it is to change the rotational motion of an object and can be calculated using the formula I = mr^2, where m is the mass of the wheel and r is the radius. Therefore, the angular acceleration of the wheel can be manipulated by changing either the torque or the moment of inertia.