Rotational motion: Find angular displacement when rotation speed is changing

[mememe1245]

Homework Statement

A torque acts on a wheel rotating at 19.8 rad/s and increases its angular speed to 23.5 rad/s in 11.2 s. Find the angle through which the wheel turns during this time.

Homework Equations

omega = theta/time

The Attempt at a Solution

23.5 - 19.8/11.2 = .33rad/s/s --- this is wrong.

 

[gneill]

Your thread title is non-descriptive of the thread content. I will change it this time.

Clearly the problem involves a change in rotation speed, so an angular acceleration is involved. You haven't presented any Relevant Equations involving acceleration.

Can you explain your attempt at solution? Use symbols rather than numbers.

 

[SteamKing]

Homework Statement

A torque acts on a wheel rotating at 19.8 rad/s and increases its angular speed to 23.5 rad/s in 11.2 s. Find the angle through which the wheel turns during this time.

Homework Equations

omega = theta/time

The Attempt at a Solution

23.5 - 19.8/11.2 = .33rad/s/s --- this is wrong.

The problem clearly states, "Find the angle ..." Is 0.33 rad/s/s how you measure an angle?

Review your equations for angular motion. There should be one which gives you the angular displacement if you know: the time, the angular velocity, and the angular acceleration.

 

[Sharath K Menon]

You found out the angular acceleration...NOT the angle present.

Try using proper required equations to find out the angle displaced

(Hint:- kinematic equations and equations for circular motions are pretty much the same

 

[HalfLostAndSearching]

To find the angular displacement, we need to use the formula:
theta = omega*t + (1/2)*alpha*t^2
Where:
theta = angular displacement
omega = initial angular velocity
alpha = angular acceleration
t = time

In this problem, we are given:
omega = 19.8 rad/s (initial angular velocity)
alpha = torque (unknown)
t = 11.2 s (time)

To find alpha, we can use the formula:
alpha = torque/mass*radius
Where:
torque = torque acting on the wheel
mass = mass of the wheel
radius = radius of the wheel

Since we are not given the mass or radius of the wheel, we cannot solve for alpha. However, we can still calculate the angular displacement by using the initial and final angular velocities given in the problem.

Substituting the values into the formula, we get:
theta = (23.5 rad/s * 11.2 s) + (1/2)(alpha)(11.2 s)^2
= 263.2 rad + (1/2)(alpha)(125.44 s^2)

Since we do not have the value for alpha, we cannot solve for the exact angular displacement. However, we can say that the wheel turns at least 263.2 radians during the given time interval.

Note: If we were given the values for mass and radius, we could solve for alpha and then calculate the exact angular displacement.