A 70 cm diameter wheel is rotating at 1 300 revolutions per minute and a small 5g mass is fixed to the outer edge of the wheel. Calculate the strength and direction of the centripetal force that is exerted on the mass.
First convert your angular speed from rpm to rad/s. You can then convert your angular speed to tangential speed with v = omega * r. (Be sure to convert that diameter into SI units!)
Newton's second law gives us F = ma, where this is centripetal acceleration, so
F = (mv^2)/r. You have m and r, and solved for v previously.
Note that this assumes a horizontal wheel.
To calculate the strength and direction of the centripetal force exerted on the mass, we need to understand the equation for centripetal force:
F = mv²/r
where:
F is the centripetal force
m is the mass
v is the velocity
r is the radius
First, let's find the velocity of the mass on the wheel. We know that the wheel is rotating at 1,300 revolutions per minute. Since the diameter of the wheel is 70 cm, the radius is half of the diameter, so r = 35 cm or 0.35 m.
To convert revolutions per minute to angular velocity (ω) in radians per second, we use the following equation:
ω = 2πn/60
where:
ω is the angular velocity
n is the number of revolutions per minute
Plugging in the values, we get:
ω = (2π * 1,300) / 60
≈ 135.3 radians per second
Next, we can calculate the linear velocity (v) using the formula:
v = ω * r
Plugging in the values:
v = 135.3 * 0.35
≈ 47.355 m/s
Now, we need to convert the mass from grams to kilograms:
m = 5g / 1000
= 0.005 kg
Finally, we can calculate the centripetal force (F):
F = mv²/r
= 0.005 * (47.355)² / 0.35
≈ 322.85 N
So, the centripetal force exerted on the mass is approximately 322.85 Newtons. The direction of the centripetal force is towards the center of the wheel, which is perpendicular to the outward direction of the mass.