What is the magnitude of the acceleration of a speck of clay on the edge of a potter's wheel turning at 44 rpm (revolutions per minute) if the wheel's diameter is 31 cm?
To find the magnitude of the acceleration of the speck of clay on the edge of the potter's wheel, we can use the following steps:
1. Convert the wheel's angular velocity from rpm to rad/s.
Given: 44 rpm
To convert from rpm to rad/s, we can use the formula:
angular velocity (ω) = (2π × frequency) / 60
Substituting the given value of angular velocity:
ω = (2π × 44) / 60
ω ≈ 4.599 rad/s
2. Calculate the linear velocity of the speck of clay on the edge of the wheel.
The linear velocity (v) can be calculated using the formula:
v = ω × r
Given: Wheel's diameter = 31 cm
Since the diameter (d) is twice the radius (r):
r = d / 2 = 31 / 2 = 15.5 cm = 0.155 m
Substituting the values of ω and r into the formula:
v = 4.599 × 0.155 ≈ 0.712 m/s
3. Determine the magnitude of the acceleration.
The magnitude of the acceleration (a) can be calculated using the formula:
a = v^2 / r
Substituting the values of v and r into the formula:
a = (0.712)^2 / 0.155 ≈ 3.27 m/s^2
Therefore, the magnitude of the acceleration of the speck of clay on the edge of the potter's wheel is approximately 3.27 m/s^2.
To find the magnitude of the acceleration of a speck of clay on the edge of a potter's wheel, we can use the formula for centripetal acceleration.
The formula for centripetal acceleration is:
a = (v^2) / r
Where:
a = centripetal acceleration
v = linear velocity
r = radius of the circular path
First, we need to find the linear velocity of the speck of clay on the edge of the potter's wheel. To do this, we can convert the given wheel's rotation rate from rpm to radians per second.
1 revolution = 2π radians
1 minute = 60 seconds
So, the wheel's rotation rate in radians per second is:
(44 rpm) * (2π radians / 1 revolution) * (1 minute / 60 seconds) = 44 * 2π / 60 radians per second
Next, we need to find the linear velocity. The linear velocity is the distance traveled per unit time, which is given by the formula:
v = ω * r
Where:
v = linear velocity
ω = angular velocity (in radians per second)
r = radius of the circular path
The radius of the circular path is half the diameter, so r = 31 cm / 2 = 15.5 cm = 0.155 m.
Finally, we can substitute the calculated linear velocity and radius into the formula for centripetal acceleration:
a = (v^2) / r
Now we can solve for a by substituting the values:
a = (v^2) / r
= [(ω * r)^2] / r
= (ω^2) * r
Substituting the values:
a = [(44 * 2π / 60)^2] * 0.155
Calculating this expression will give us the magnitude of the acceleration of the speck of clay on the edge of the potter's wheel.
Radius = R = 0.31/2 meter
omega = angular velocity = 44 revs/min * 1 min/60 s * 2 pi rad/rev
= 4.61 rad/sec
so
Ac = omega^2 R = (4.61)^2 ^ 0.155