Answer:
I = 113.014 kg.m^2
m = 2075.56 kg
wf = 3.942 rad/s
Explanation:
Given:
- The constant Force applied F = 300 N
- The radius of the wheel r = 0.33 m
- The angular acceleration α = 0.876 rad / s^2
Find:
(a) What is the moment of inertia of the wheel (in kg · m2)?
(b) What is the mass (in kg) of the wheel?
(c) The wheel starts from rest and the tangential force remains constant over a time period of t= 4.50 s. What is the angular speed (in rad/s) of the wheel at the end of this time period?
Solution:
- We will apply Newton's second law for the rotational motion of the disc given by:
F*r = I*α
Where, I: The moment of inertia of the cylindrical wheel.
I = F*r / α
I = 300*0.33 / 0.876
I = 113.014 kg.m^2
- Assuming the cylindrical wheel as cylindrical disc with moment inertia given as:
I = 0.5*m*r^2
m = 2*I / r^2
Where, m is the mass of the wheel in kg.
m = 2*113.014 / 0.33^2
m = 2075.56 kg
- The initial angular velocity wi = 0, after time t sec the final angular speed wf can be determined by rotational kinematics equation 1:
wf = wi + α*t
wf = 0 + 0.876*(4.5)
wf = 3.942 rad/s
We can use kinematics here if we assume a constant acceleration (not realistic, but they want a single value answer, so it's implied). We know final velocity, vf, is 1.0 m/s, and we cover a distance, d, of 0.47mm or 0.00047 m (1m = 1000mm for conversion). We also can assume that the flea's initial velocity, vi, is 0 at the beginning of its jump. Using the equation vf^2 = vi^2 + 2ad, we can solve for our acceleration, a. Like so: a = (vf^2 - vi^2)/2d = (1.0^2 - 0^2)/(2*0.00047) = 1,064 m/s^2, not bad for a flea!
This is very good conceptual question and can clear your doubts regarding work-energy theorem.
Whenever force is perpendicular to the direction of the motion, work done by that force is zero.
According to work-energy theorem,
Work done by all the force = change in kinetic energy.
here, work done = 0.
Therefore,
0=change in kinetic energy
This means kinetic energy remains constant.
Hope this helps
Answer:
Explanation:
As the disc is unrolling from the thread then at any moment of the time
We have force equation as
also by torque equation we can say
Now we have
Also from above equation the tension force in the string is
Answer:
An Element
Explanation:
Such substance cannot be an element because an element cannot be chemically disintegrated (i.e it cannot be disintegrated via chemical reaction).
