# Solve Time for Wheel C Rotational Speed 108.3 rev/min in Belt Drive Problem

• sheri1987
In summary, to determine the time at which wheel C reaches a rotational speed of 108.3 rev/min, we must first clarify some details about the system and then use the appropriate equations to solve for the time.
sheri1987

## Homework Statement

Wheel A of radius ra = 6.5 cm is coupled by belt B to wheel C of radius rc = 32.8 cm. Wheel A increases its angular speed from rest at time t = 0 s at a uniform rate of 6.2 rad/s2. At what time will wheel C reach a rotational speed of 108.3 rev/min, assuming the belt does not slip?

## Homework Equations

wf=w(initial)+ alpha x time

## The Attempt at a Solution

I used a=alpha x radius, twice to solve for alpha of ra and rc and then i want to use the wf=w(initial) +alpha x time..but which alpha do I use, ra or rc?

I would first clarify some details about the problem to ensure that I am using the correct equations and values. Here are some questions I would ask:

1) Is the belt B connected to the outer edge of wheel A and the inner edge of wheel C, or vice versa?
2) Is the belt B a fixed length, or does it have some elasticity that may affect the speed of wheel C?
3) Is the initial speed of wheel A zero, or is it rotating at a constant speed before the experiment starts?
4) Is the rotational speed of wheel C increasing or decreasing, and at what rate?

Once these details are clarified, I would use the appropriate equations to solve for the time when wheel C reaches a rotational speed of 108.3 rev/min. If the belt is connected as I described in question 1, then I would use the equation wf = w(initial) + alpha x time for wheel C, using the alpha value calculated from the radius of wheel C. If the belt has some elasticity, then I may need to consider the acceleration of the belt as well.

In general, when solving for rotational motion in systems with multiple components, it is important to consider the relationships between the components and the effects they may have on each other.

To solve this problem, you will need to use the equation w_f = w_i + alpha x t, where w_f is the final angular speed, w_i is the initial angular speed, alpha is the angular acceleration, and t is the time. In this case, you know the final angular speed (108.3 rev/min), the initial angular speed (0 rad/s), and the angular acceleration (6.2 rad/s^2). You also know the radius of wheel C (32.8 cm). Using this information, you can solve for the time (t) it takes for wheel C to reach a rotational speed of 108.3 rev/min. You do not need to use the radius of wheel A in this calculation.

## 1. What is the formula for solving time in a belt drive problem?

The formula for solving time in a belt drive problem is T = 2πr/v, where T is time, π is pi (approximately 3.14), r is the radius of the wheel, and v is the rotational speed in revolutions per minute (rev/min).

## 2. What is the unit of measurement for rotational speed?

The unit of measurement for rotational speed is revolutions per minute (rev/min).

## 3. How do I convert rev/min to radians per second?

To convert rev/min to radians per second, multiply the rev/min value by 2π/60. This will give you the value in radians per second.

## 4. Can I use the same formula to solve for time in a belt drive problem if the rotational speed is given in radians per second?

Yes, you can use the same formula to solve for time in a belt drive problem if the rotational speed is given in radians per second. However, make sure to use the appropriate unit of measurement for the radius (r) in the formula.

## 5. What other factors should I consider when solving for time in a belt drive problem?

When solving for time in a belt drive problem, it is important to also consider the distance between the wheels, the type of belt being used, and any other external factors that may affect the speed and efficiency of the belt drive system.

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