Answer:
a. 
b. 
Explanation:
I have attached an illustration of a solid disk with the respective forces applied, as stated in this question.
Forces applied to the solid disk include:

Other parameters given include:
Mass of solid disk, 
and radius of solid disk, 
a.) The formula for determining torque (
), is 
Hence the net torque produced by the two forces is given as a summation of both forces:

b.) The angular acceleration of the disk can be found thus:
using the formula for the Moment of Inertia of a solid disk;

where
= Mass of solid disk
and
= radius of solid disk
We then relate the torque and angular acceleration (
) with the formula:

<h3>
Answer:</h3>
225 meters
<h3>
Explanation:</h3>
Acceleration is the rate of change in velocity of an object in motion.
In our case we are given;
Acceleration, a = 2.0 m/s²
Time, t = 15 s
We are required to find the length of the slope;
Assuming the student started at rest, then the initial velocity, V₀ is Zero.
<h3>Step 1: Calculate the final velocity, Vf</h3>
Using the equation of linear motion;
Vf = V₀ + at
Therefore;
Vf = 0 + (2 × 15)
= 30 m/s
Thus, the final velocity of the student is 30 m/s
<h3>Step 2: Calculate the length (displacement) of the slope </h3>
Using the other equation of linear motion;
S = 0.5 at + V₀t
We can calculate the length, S of the slope
That is;
S = (0.5 × 2 × 15² ) - (0 × 15)
= 225 m
Therefore, the length of the slope is 225 m
Answer:
(a). The initial speed of the arrow is 49.96 m/s.
(b). The angle is 39.90°.
Explanation:
Given that,
Horizontal distance = 230 m
Time t = 6 sec
Vertical distance = 16 m
We need to calculate the horizontal component
Using formula of horizontal component

Put the value into the formula

.....(I)
We need to calculate the height
Using vertical component

Put the value in the equation


.....(II)
Dividing equation (II) and (I)




(a). We need to calculate the initial speed
Using equation (I)

Put the value into the formula


(b). We have already calculate the angle.
Hence, (a). The initial speed of the arrow is 49.96 m/s.
(b). The angle is 39.90°.
Answer:
v = 10 m/s
Explanation:
Let's assume the wheel does not slip as it accelerates.
Energy theory is more straightforward than kinematics in my opinion.
Work done on the wheel
W = Fd = 45(12) = 540 J
Some is converted to potential energy
PE = mgh = 4(9.8)12sin30 = 235.2 J
As there is no friction mentioned, the remainder is kinetic energy
KE = 540 - 235.2 = 304.8 J
KE = ½mv² + ½Iω²
ω = v/R
KE = ½mv² + ½I(v/R)² = ½(m + I/R²)v²
v = √(2KE / (m + I/R²))
v = √(2(304.8) / (4 + 0.5/0.5²)) = √101.6
v = 10.07968...
Answer:
The force of the impact would be smaller
Explanation: Examples:
If the force is big then the time would be small (2500N of Force = 10 seconds)
If the force is small then the time would be big (250N of Force = 50 seconds)
Impulse/Collision -> [Ft] = [M (vf-vo)] <- Change in momentum