We will use the equations of rotational kinematics,
(A)
(B)
Here, 
and 
denote the final and initial angular displacements, respectively, whereas 
and 
represent final and initial angular velocities, and 
is the angular acceleration.
We are provided with 
and 
.
By substituting these values into equation (A), we have
Now, using equation (B),
This indicates that the wheel's angular speed at the 4.20-second mark is 36.7 rad/s.
Answer:
407 steps
Explanation:
Based on the question,
P = mgh/t........... Equation 1
Where P stands for power, m is mass, g denotes gravity, h is height, and t represents time.
Rearranging the equation to solve for h, we have:
h = Pt/mg............. Equation 2
Providing values: P = 746 W, t = 1 minute = 60 seconds, m = 70 kg.
Given constant: g = 9.8 m/s²
By substituting into equation 2
h = 746(60)/(70×9.8)
h = 44760/686
h = 65.25 m
h = 6525 cm
Calculating number of steps: 6525/16
The resulting number of steps = 407 steps
For this issue, the answer is clarified as the system takes in energy (+). The surroundings contribute 84 KJ of work. Whenever a system is receiving work from its surroundings, the value will be positive. Therefore, it sums to 12.4 KJ + 4.2 = 16.6 KJ.
The angle formed with the positive x-axis is 120 degrees. We can assume that this angle is determined in a counterclockwise direction from the positive x-axis. The x-component of the vector can be calculated as: x-component = 10 cos(120) = -5. The vector's y-component is determined as: y-component = 10 sin(120) = 8.66. The x-component equates to -5 while the y-component equals 8.66.
The acceleration is calculated using the formula a= change in velocity/time. Here, it becomes A=10-0/2, simplifying to A=10/2, resulting in A=5 m/s².
