Calculating Rotational Speed for Wheel C: 240.7 rev/min

[hatingphysics]

Wheel A of radius ra = 14.6 cm is coupled by belt B to wheel C of radius rc = 28.8 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 240.7 rev/min, assuming the belt does not slip?

I did ...Vta = Vtc, but stil didint get it. i got the Vtc
value and divided that by raduis of A to get w for a. then
divided the acceleration by the w for a, but my time is
still wrong!

 

[berkeman]

Sounds like you are basically using the correct approach. Can you please post your calculations (including units) so we can see if it's just a math error?

 

[kyle8921]

I would approach this problem by first identifying the given values and the unknown variable that needs to be solved for. In this case, the given values are the rotational speed of wheel C (240.7 rev/min), the radius of wheel A (14.6 cm), the radius of wheel C (28.8 cm), and the angular acceleration of wheel A (7.1 rad/s^2). The unknown variable is the time at which wheel C reaches a rotational speed of 240.7 rev/min.

Next, I would use the formula Vta = Vtc, which states that the tangential velocity of wheel A is equal to the tangential velocity of wheel C. Using this formula, I can calculate the tangential velocity of wheel A by dividing the rotational speed of wheel C (240.7 rev/min) by the radius of wheel C (28.8 cm). This gives a tangential velocity of 8.35 cm/s for wheel A.

Then, I would use the formula w = a*t, where w is the angular velocity, a is the angular acceleration, and t is the time. Since we know the angular acceleration (7.1 rad/s^2) and we want to solve for t, we can rearrange the formula to t = w/a. Plugging in the calculated tangential velocity for wheel A (8.35 cm/s) and the given angular acceleration (7.1 rad/s^2), we get a time of approximately 0.117 seconds.

Therefore, wheel C will reach a rotational speed of 240.7 rev/min at approximately 0.117 seconds, assuming the belt does not slip. It is important to double check the units and make sure they are consistent throughout the calculations. Additionally, any rounding should be done at the end to ensure accuracy in the final answer.