A particles of mass 10-2kg is fixed at the tip of a fan blade which rotates at an angular velocity of 100rad-1.if the radius of the blade is 0.2m,then what is the centripetal force?
Well, isn't this a "tip"-top question! Let's calculate the centripetal force and "fan" the flames of knowledge!
The centripetal force is given by the equation:
F = m * ω^2 * r
Where:
- F is the centripetal force,
- m is the mass,
- ω is the angular velocity, and
- r is the radius.
Plugging in the values given:
- m = 10^-2 kg,
- ω = 100 rad/s, and
- r = 0.2 m,
We can calculate the force:
F = (10^-2 kg) * (100 rad/s)^2 * (0.2 m)
Now, let's crunch the numbers:
F = 10^-2 * 100^2 * 0.2
F = 10^-2 * 10000 * 0.2
F = 2 N
Voila! The centripetal force acting on the particle at the tip of the fan blade is 2 Newtons. Keep "blading" through those physics problems!
To find the centripetal force acting on the particle, we can use the formula:
Centripetal force = mass × angular velocity² × radius
Given:
Mass (m) = 10^(-2) kg
Angular velocity (ω) = 100 rad/s
Radius (r) = 0.2 m
Plugging in the values, we get:
Centripetal force = (10^(-2) kg) × (100 rad/s)² × 0.2 m
First, let's calculate the squared value of the angular velocity:
(100 rad/s)² = 10000 rad²/s²
Now, let's substitute the values back into the formula:
Centripetal force = (10^(-2) kg) × 10000 rad²/s² × 0.2 m
Next, let's simplify the expression:
Centripetal force = (10^(-2) kg) × 2000 rad²/s²
Finally, let's perform the multiplication:
Centripetal force = 2 kg × 2000 rad²/s²
Centripetal force = 4000 N
Therefore, the centripetal force acting on the particle is 4000 Newtons.
To find the centripetal force, we can use the formula:
Centripetal Force = Mass × Angular Velocity² × Radius
Given:
Mass (m) = 10^(-2) kg
Angular Velocity (ω) = 100 rad/s
Radius (r) = 0.2 m
Let's calculate the centripetal force step by step:
Step 1: Calculate the square of the angular velocity
Angular Velocity² = (100 rad/s)² = 10,000 rad²/s²
Step 2: Multiply the square of the angular velocity by the mass and radius
Centripetal Force = (10^(-2) kg) × (10,000 rad²/s²) × (0.2 m)
Step 3: Simplify the expression
Centripetal Force = 10 × 10,000 × 0.2 kg rad²/s² m
Step 4: Calculate the final result
Centripetal Force = 2,000 N
Therefore, the centripetal force acting on the particle is 2,000 Newtons.