A rotating turntable of mass 200g and
radius 10 cm is uniformly accelerated from rest to attain
it's maximum velocity of 33 and half revolution per
minute through an angular displacement of 240 degree .
Determine the (1). uniform angular acceleration. (2).time
of acceleration
mass and radius are spurious information
convert 33.5 rpm to rad/s ... multiply by π and divide by 60
... divide by 2 to find average angular velocity during acceleration
convert 240º to radians ... multiply by π and divide by 360
... divide result by average angular velocity to find acceleration time
acceleration is max velocity divided by acceleration time
u mean
(33.5*3.142)/60=1.75
Then
1.7/2=0878(angular velocity)
Please is that the answer
To determine the uniform angular acceleration of the turntable, we can use the formula:
angular acceleration (α) = final angular velocity (ωf) - initial angular velocity (ωi) / time (t)
Given:
- Mass of the turntable (m) = 200g = 0.2 kg
- Radius of the turntable (r) = 10 cm = 0.1 m
- Maximum velocity (v) = 33 and a half revolution per minute
- Angular displacement (θ) = 240 degrees
First, we need to convert the maximum velocity from revolutions per minute to radians per second:
1 revolution = 2π radians
33 and a half revolutions = 33.5 * 2π radians
To calculate the angular velocity (ωf) in radians per second, we divide the above value by 60 (60 seconds per minute):
ωf = (33.5 * 2π) / 60
Next, we need to find the initial angular velocity (ωi). Since the turntable starts from rest, ωi = 0.
The time (t) can be found using the formula:
θ = ωi * t + 0.5 * α * t^2
Given θ = 240 degrees, we need to convert it to radians:
θ = 240 * (π / 180)
We can rearrange the formula to solve for time (t):
0.5 * α * t^2 = θ
Substituting the known values:
0.5 * α * t^2 = 240 * (π / 180)
Now, we can solve for time (t):
t^2 = (240 * (π / 180)) / (0.5 * α)
t^2 = (4π / 3) / α
To find the uniform angular acceleration (α), we use the fact that the maximum velocity of a rotating object is related to its angular acceleration:
v = α * r
Substituting the known values:
33.5 * 2π = α * 0.1
Now we have two equations:
1. t^2 = (4π / 3) / α
2. 33.5 * 2π = α * 0.1
Using the second equation, we can solve for α:
α = (33.5 * 2π) / 0.1
Finally, substitute this value of α into the first equation to solve for t^2:
t^2 = (4π / 3) / ((33.5 * 2π) / 0.1)
Simplifying the equation gives us t^2:
t^2 = (4 * 0.1) / (3 * 33.5)
Solving for t^2:
t^2 = 0.004776 -> t ≈ 0.069 s (approx.)
Therefore, the answers are:
(1) The uniform angular acceleration is α ≈ 209.4 rad/s^2 (approx.).
(2) The time of acceleration is t ≈ 0.069 seconds (approx.).