A constant force of 40newton is applied tangentally to the rim of the wheel with 20cetimetre radius the wheel hs moment of intial 30kg find (a)angular acceleration (b)angular speed after 4second frm rest (c)d number of revolution made in(d)show that d work done of d wheel in dis 4seconds is equal to d kinetic energy of d wheel after 4seconds.
Seems to be a bad typing day
hs moment of intial 30kg
Suspect you mean moment of inertia but the units are wrong.
If it is I = 30 kg m^2
then torque = I alpha
alpha = angular acceleration
= 40 * 0.20 N m / 30 kg m^2
omega = alpha * t
theta = (1/2) alpha t^2
number of revs = theta/2pi
work done = Torque * theta
should be (1/2) I omega^2
To solve this problem, we need to use equations from rotational dynamics. Let's break down each part:
(a) Angular acceleration (α) can be found using the formula:
τ = I * α
Where τ is the torque applied, I is the moment of inertia, and α is the angular acceleration.
In this case, the torque (τ) can be calculated as the product of the applied force (F) and the radius (r) of the wheel:
τ = F * r
Substituting the given values:
τ = 40 N * 0.2 m
Next, we need to find the moment of inertia (I) for a wheel rotating about its axis. For a solid disc, the moment of inertia 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.
Given that the moment of inertia (I) is 30 kg, we can solve for the mass (m):
I = (1/2) * m * (0.2 m)^2
30 kg = (1/2) * m * 0.04 m^2
m = 30 kg / 0.02 m
Now that we have the mass, we can calculate the angular acceleration (α) using the formula:
α = τ / I
Substituting the values, we get:
α = (40 N * 0.2 m) / [(1/2) * (30 kg / 0.02 m) * 0.04 m^2]
(b) The angular speed (ω) after 4 seconds can be found using the equation:
ω = ω0 + α * t
Where ω0 is the initial angular speed (which is 0 in this case), α is the angular acceleration, and t is the time.
Substituting the known values, we get:
ω = α * t
(c) To find the number of revolutions made in 4 seconds, we can use the formula:
θ = ω0 * t + (1/2) * α * t^2
Where θ is the angle in radians.
But since the initial angular speed (ω0) is 0, the equation simplifies to:
θ = (1/2) * α * t^2
To convert the angle from radians to revolutions, we divide by 2π:
Number of revolutions = θ / (2π)
(d) To show that the work done on the wheel in 4 seconds is equal to the kinetic energy of the wheel after 4 seconds, we need to calculate both quantities.
The work done (W) on the wheel can be calculated using the formula:
W = τ * θ
Where τ is the torque and θ is the angle in radians.
The kinetic energy (KE) can be calculated using the formula:
KE = (1/2) * I * ω^2
Where I is the moment of inertia and ω is the angular speed.
By calculating these quantities and comparing them, we can see if they are equal.