# Physics

posted by .

A lawn mower has a flat, rod-shaped steel blade that rotates about its center. The mass of the blade is 0.65kg and its length is 0.55m. What is the rotational energy of the blade at its operating angular speed of 3450 rpm? If all of the rotational kinetic energy of the blade could be converted to gravitational potential energy, to what height would the blade rise?

• Physics -

Use the rotational energy equation, E = 0.5Iω², where I is the moment of inertia for a long thin rod with an axis through it's midpoint (I = (1/12)mL²).

E = 0.5Iω²
E = 0.5 [1/12)mL²] ω²
E = (1/24) mL² ω²

Find ω by multiplying the rpm by 2π and then dividing by 60 to put units into rad/sec (or multiply ω by π/30)

3450 * 2π = 21 676.9... rad/min
(21 676.9... rad/min)/60 = 361.28... rad/sec

Insert into energy eqn and solve

E = (1/24) mL² (361.28...rad/s)²
E = (1/24)(0.65kg)(0.55m²)(361.28...rad/s)²
E = ~1069 J

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### Physics

Consider a 52-cm-long lawn mower blade rotating about its center at 3390 rpm. (a) Calculate the linear speed of the tip of the blade. (b) If safety regulations require that the blade be stoppable within 3.0 s, what minimum angular …
2. ### Physics

A certain type of propeller blan can be modeled as a thin uniform bar 2.50 m long and of mass 24.0 kg that is free to rotate about a frictionless axle perpendicular to the bar at its midpoint. if a technician strikes this blade with …
3. ### physics

a certain type of propeller blade can be modeled as a thin uniform bar 2.5 m long and of mass 24 kg that is free to rotate about a frictionless axle perpendicular to the bar at its midpoint. if a technician strikes this blade witha …
4. ### physics

An electric saw uses a circular spinning blade to slice through wood. When you start the saw, the motor needs 6 seconds of constant angular acceleration to bring the blade to its full angular velocity. If you change the blade so that …
5. ### Physics

An 83.2-kg propeller blade measures 2.24m end to end. Model the blade as a thin rod rotating about its center of mass. It's initially turning at 175rpm. Find the blade's angular momentum, the tangential speed at the blade tip, and …
6. ### physics

An 83.2-kg propeller blade measures 2.24m end to end. Model the blade as a thin rod rotating about its center of mass. It's initially turning at 175rpm. Find the blade's angular momentum, the tangential speed at the blade tip, and …
7. ### physics

An 83.2-kg propeller blade measures 2.24m end to end. Model the blade as a thin rod rotating about its center of mass. It's initially turning at 175rpm. Find the blade's angular momentum, the tangential speed at the blade tip, and …
8. ### Physics

Consider a 59-cm-long lawn mower blade rotating about its center at 2990 rpm. (a) Calculate the linear speed of the tip of the blade. (b) If safety regulations require that the blade be stoppable within 3.0 s, what minimum angular …
9. ### Physics

A helicopter propeller blade starts from rest and experiences a constant angular acceleration of 25.0 rad/s2. Find the speed of a point on the blade 4.00 m from the axis of rotation when the blade has completed 20 revolutions.
10. ### Physics

13. The graph at right shows the angular velocity as a function of time for the blade of a fan. The blade moves in a circular path. a. If θ = 0 rad at t = 0 s, what is the blade’s position at t = 1.5 s?

More Similar Questions

Post a New Question