A turntable rotating at 33 1/3 rpm is shut off. It brakes with constant angular deceleration and stops in 26 seconds. Find the average angular acceleration. I took 33 1/3 divided by 26 and then tried to convert to rad/s^2 but I keep getting the wrong answer. How should I approach this problem?
change rpm to rad/sec
33.33 r/min*2PI rad/rev*1min/60sec
=33.33*2PI/60 rad/sec
a=changev/time=(vf-Vi)/time=-above/26
To find the average angular acceleration, you need to use the formula:
Ang. Acc. = (Final angular velocity - Initial angular velocity) / time
In this case, the initial angular velocity is given as 33 1/3 rpm. To convert it to radians per second (rad/s), you need to use the conversion factor: 1 rpm = (2π/60) rad/s.
Let's begin by converting the initial angular velocity from rpm to rad/s:
Initial angular velocity = (33 1/3 rpm) x (2π/60 rad/s)
= (33 1/3 x 2π) / 60 rad/s
= (33 1/3 x π) / 30 rad/s
Now, we can use the given information that the turntable stops in 26 seconds. The final angular velocity is 0, as the turntable comes to a stop.
Final angular velocity = 0 rad/s
Now, we can substitute the values into the formula:
Avg. Ang. Acc. = (Final angular velocity - Initial angular velocity) / time
= (0 - [(33 1/3 x π) / 30]) / 26 rad/s^2
Simplifying the expression further will give you the correct value of the average angular acceleration.
To find the average angular acceleration, we need to first determine the initial angular velocity and the final angular velocity.
Given:
Initial angular velocity, ω₁ = 33 1/3 rpm
Time taken to stop, t = 26 seconds
To solve this problem, follow these steps:
Step 1: Convert the initial angular velocity from rpm to rad/s.
We know that 1 rpm is equal to (2π/60) rad/s. Therefore, the initial angular velocity ω₁ in rad/s is:
ω₁ = (33 1/3) * (2π/60) rad/s
Step 2: Find the final angular velocity, ω₂.
Since the turntable stops, the final angular velocity ω₂ is zero.
Step 3: Use the equation of angular motion:
ω₂ = ω₁ + α * t
Where:
ω₂ = final angular velocity (0 rad/s)
ω₁ = initial angular velocity (in rad/s)
α = average angular acceleration
t = time taken to stop (in seconds)
Rearranging the equation to solve for α, we have:
α = (ω₂ - ω₁) / t
Note: ω₂ = 0, so the equation further simplifies to:
α = -ω₁ / t
Step 4: Substitute the values into the equation and calculate the average angular acceleration:
α = -(ω₁) / t
Now, let's perform the calculations: