A compact disk, which has a diameter of 12.0 cm, speeds up uniformly from zero to 4.40 rev/s in 3.20 s
What is the tangential acceleration of a point on the outer rim of the disk at the moment when its angular speed is 3.00 {rev/s}?
To find the tangential acceleration of a point on the outer rim of the disk, we can use the formula:
a_t = r * α
where a_t is the tangential acceleration, r is the radius of the disk, and α is the angular acceleration.
First, let's find the angular acceleration using the formula:
α = (ω_f - ω_i) / t
where ω_f is the final angular speed, ω_i is the initial angular speed, and t is the time taken to reach the final angular speed.
Given:
ω_f = 4.40 rev/s
ω_i = 0 rev/s
t = 3.20 s
Plugging in the values, we have:
α = (4.40 rev/s - 0 rev/s) / 3.20 s
Calculating this:
α = 1.375 rev/s²
Now, we need to find the radius of the disk. The diameter of the disk is given as 12.0 cm, so the radius can be calculated as half of the diameter:
r = 12.0 cm / 2
Converting the radius to meters:
r = 0.06 m
Finally, we can calculate the tangential acceleration:
a_t = r * α
Plugging in the values:
a_t = 0.06 m * 1.375 rev/s²
Converting the tangential acceleration to m/s² by multiplying by 2π (since there are 2π radians in one revolution):
a_t = 0.06 m * 1.375 rev/s² * 2π rad/rev
Calculating this:
a_t ≈ 1.631 m/s²
So, the tangential acceleration of a point on the outer rim of the disk when its angular speed is 3.00 rev/s is approximately 1.631 m/s².
To find the tangential acceleration of a point on the outer rim of the disk, we can use the formula:
Tangential acceleration = Radius × Angular acceleration
First, we need to find the radius of the disk. The diameter is given as 12.0 cm, so the radius is half of that:
Radius = Diameter / 2
Radius = 12.0 cm / 2
Radius = 6.0 cm = 0.06 m
Next, let's find the angular acceleration. The angular acceleration is the change in angular velocity divided by the time taken:
Angular acceleration = (Final angular velocity - Initial angular velocity) / Time
Given:
Initial angular velocity = 0 rev/s
Final angular velocity = 4.40 rev/s
Time = 3.20 s
Angular acceleration = (4.40 rev/s - 0 rev/s) / 3.20 s
Angular acceleration = 1.375 rev/s^2
Now, we have the radius (0.06 m) and the angular acceleration (1.375 rev/s^2) for the formula. To find the tangential acceleration at the moment when the angular speed is 3.00 rev/s, we can substitute these values into the formula:
Tangential acceleration = Radius × Angular acceleration
Tangential acceleration = 0.06 m × 1.375 rev/s^2
Tangential acceleration = 0.0825 m/s^2
Therefore, the tangential acceleration of a point on the outer rim of the disk, when its angular speed is 3.00 rev/s, is 0.0825 m/s^2.
tangential acc=radial acc*radius
radial acc=4.4*2PI/3.2