What is the linear acceleration of a point on the rim of a 38 cm-diameter record rotating at 33 1/3 rev/min?
To find the linear acceleration of a point on the rim of a rotating object, such as a record, you can use the following steps:
Step 1: Convert the diameter of the record from centimeters to meters:
To convert cm to m, divide by 100.
Given diameter = 38 cm.
Diameter in meters = 38 cm ÷ 100 = 0.38 m.
Step 2: Convert the given rotational speed from revolutions per minute (rpm) to radians per second (rad/s):
To convert rpm to rad/s, multiply by 2π/60.
Given rotational speed = 33 1/3 rev/min.
Rotational speed in rad/s = 33 1/3 rev/min × 2π/60 = 2π/3 rad/s.
Step 3: Calculate the radius of the record:
The radius is half of the diameter.
Radius = 0.38 m ÷ 2 = 0.19 m.
Step 4: Calculate the linear velocity of a point on the rim:
The linear velocity of a point on the rim is equal to the product of the rotational speed and the radius.
Linear velocity = rotational speed × radius.
Linear velocity = (2π/3 rad/s) × 0.19 m.
Step 5: Calculate the linear acceleration of a point on the rim:
The linear acceleration of a point on the rim is equal to the product of the linear velocity and the rotational speed.
Linear acceleration = linear velocity × rotational speed.
Linear acceleration = ((2π/3 rad/s) × 0.19 m) × (2π/3 rad/s).
After performing the calculations, you will find the linear acceleration.
To find the linear acceleration of a point on the rim of a rotating object, we need to use the formula:
Linear acceleration = Radius * Angular acceleration
First, we need to find the radius of the record. We are given the diameter, which is 38 cm. The radius (r) is half of the diameter.
r = diameter / 2
r = 38 cm / 2
r = 19 cm
Next, we need to find the angular acceleration. Since we are given the speed of rotation in terms of revolutions per minute (rev/min), we need to convert it to radians per second (rad/s).
1 revolution = 2π radians
So, 33 1/3 rev/min is equivalent to:
33 1/3 rev/min * (2π radians/1 revolution) = 33 1/3 * 2π radians/min
To convert minutes to seconds, we need to multiply by 1/60:
33 1/3 * 2π * (1/60) radians/s
Now we have the angular acceleration in radians per second (rad/s).
Finally, we can calculate the linear acceleration:
Linear acceleration = Radius * Angular acceleration
Linear acceleration = 19 cm * [33 1/3 * 2π * (1/60) radians/s]
By simplifying the expression, we can find the final numerical value.
Note: It's common practice to convert all the units to the same system, such as meters and seconds, to obtain the answer in a consistent unit.
v^2/r=w^2*r
w=33.3*2PI/60 rad/sec
r=.19m
w^2 *r = ????