Wheel A of radius ra = 6.1 cm is coupled by belt B to wheel C of radius rc = 33.3 cm. Wheel A increases its angular speed from rest at time t = 0 s at a uniform rate of 7.1 rad/s2. At what time will wheel C reach a rotational speed of 119.3 rev/min, assuming the belt does not slip?

To solve this problem, we need to find the time it takes for wheel C to reach a rotational speed of 119.3 rev/min.

Step 1: Convert the given rotational speed of wheel C from rev/min to rad/s.
- We know that 1 rev = 2π rad, and 1 min = 60 s.
- So, to convert from rev/min to rad/s, we can use the following formula: rotational speed in rad/s = (rotational speed in rev/min) * (2π rad/rev) * (1 min/60 s).

Let's calculate:
Rotational speed of C in rad/s = 119.3 rev/min * (2π rad/rev) * (1 min/60 s)
= 12.5 rad/s

Step 2: Find the angular acceleration of wheel A.
- We are given that the angular speed increases at a uniform rate of 7.1 rad/s^2. Therefore, the angular acceleration is 7.1 rad/s^2.

Step 3: Use the kinematic equation to find the time taken by wheel C to reach the desired rotational speed.
- The kinematic equation that relates angular acceleration, initial angular speed, time, and final angular speed is: final angular speed = initial angular speed + (angular acceleration * time).
- Rearranging the equation, we get: time = (final angular speed - initial angular speed) / angular acceleration.

Let's substitute the given values:
final angular speed = 12.5 rad/s
initial angular speed = 0 rad/s (since wheel A starts from rest)
angular acceleration = 7.1 rad/s^2

time = (12.5 rad/s - 0 rad/s) / 7.1 rad/s^2
= 1.76 s

Therefore, wheel C will reach a rotational speed of 119.3 rev/min at approximately 1.76 seconds.

To find the time at which wheel C reaches a rotational speed of 119.3 rev/min, we can follow these steps:

Step 1: Convert the rotational speed of wheel C from rev/min to rad/s.
Since there are 2π radians in one revolution and 60 seconds in one minute, we can use the following conversion factor:
119.3 rev/min * (2π rad/1 rev) * (1 min/60 s) = 12.5 rad/s.

Step 2: Use the angular acceleration and initial angular speed of wheel A to find the time it takes for wheel A to reach the same rotational speed as wheel C.
The angular acceleration of wheel A is given as 7.1 rad/s^2, and since wheel A starts from rest, the initial angular speed ωa is 0 rad/s. We can use the following equation to find the time t:
ωa = ω0 + αt,
where ωa is the angular speed of wheel A at time t, ω0 is the initial angular speed of wheel A, α is the angular acceleration of wheel A, and t is the time.
Plugging in the known values, we have:
12.5 rad/s = 0 + 7.1 rad/s^2 * t.
Simplifying the equation, we get:
7.1t = 12.5 rad/s.
Solving for t, we obtain:
t = 12.5 rad/s / 7.1 rad/s^2 = 1.76056338028 s.

Therefore, wheel C will reach a rotational speed of 119.3 rev/min at approximately 1.76 seconds.