A 1000-kg car has four 10-kg wheels. What fraction of the total kinetic energy of the
car is due to rotation of the wheels? Assume that the wheels have the same rotational inertia as disks
of the same mass and size. Explain why you do not need to know the radius of the wheels?
0.020
where is the answer Ashik i didn't find it also, we will fail :(
Where is the answer Madarchhodd
To find the fraction of the total kinetic energy of the car due to the rotation of the wheels, we need to compare the rotational kinetic energy (KE_r) of the wheels to the total kinetic energy (KE_total) of the car.
The rotational kinetic energy of an object can be calculated using the formula:
KE_r = (1/2) * I * ω^2,
where I is the rotational inertia (also known as moment of inertia) and ω is the angular velocity.
In this case, the wheels are assumed to have the same rotational inertia as disks of the same mass and size. The rotational inertia of a solid disk can be calculated using the formula:
I = (1/2) * m * r^2,
where m is the mass of the wheel and r is the radius of the wheel.
However, the question states that we do not need to know the radius of the wheels. This is because the fraction of the total kinetic energy due to rotation of the wheels can be determined by comparing the rotational kinetic energy of the wheels to the total kinetic energy of the car, regardless of the actual value of the radius.
Since KE_r = (1/2) * I * ω^2, the rotational kinetic energy depends on the rotational inertia (I) and the square of the angular velocity (ω^2). The radius does not appear in the expression for the rotational kinetic energy. Thus, the fraction of the total kinetic energy due to rotation of the wheels can be calculated without the need to know the radius of the wheels.
b) because the I= 1/2 mr^2 w^2
w^2= v^2/r^2 so the "r"s cancel out