# What is the torque exerted by the flywheel on the machine?

• traviata
In summary, flywheels are large, massive wheels that store energy and can release it quickly for high-power tasks. An industrial flywheel with a 2.0 m diameter and a mass of 260 kg has a maximum angular velocity of 1400 rpm. When disconnected from the motor, it delivers half of its stored energy in 2.5 seconds. To find the average power delivered to the machine and the torque exerted by the flywheel, the equation P=τ⋅ω can be used. However, since ω is not constant in this case, another equation, analogous to linear systems, may be needed to solve for the torque.
traviata

## Homework Statement

Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 2.0 m diameter and a mass of 260 kg . Its maximum angular velocity is 1400 rpm .
1. The flywheel is disconnected from the motor and connected to a machine to which it will deliver energy. Half the energy stored in the flywheel is delivered in 2.5 s . What is the average power delivered to the machine?
2. How much torque does the flywheel exert on the machine?

P=τ⋅ω

## The Attempt at a Solution

From working out earlier parts of the problem, I already have:

P = ΔE/Δt = ½Kmax/Δt = 1/8*m(ωr)2/Δt = 1/8*(260kg)*(146.61rad/s*1.0m)2 = 2.794*105 W

Mastering Physics marks this as correct. However, when I solve for torque in terms of power and angular velocity

τ = P/ω = 2.794*105 W / 146.61 rad/s = 1905.9 N*m

Master Physics marks 1900 N*m (it requires 2 significant figures), as incorrect. Any suggestions?

traviata said:
τ = P/ω
Will ω be constant?

ω is not constant, as the kinetic energy of the flywheel changes.

traviata said:
ω is not constant, as the kinetic energy of the flywheel changes.
So what value can you use in P/ω?

Are you saying I can't use ω because it's not constant. Is there another equation I have to use?

traviata said:
Are you saying I can't use ω because it's not constant. Is there another equation I have to use?
Rotational systems such as this are highly analogous to linear systems.
If you had a moving mass that loses half its (known) KE in a known time under constant force, could you find that force?

## 1. What is torque?

Torque is a measure of the force that causes an object to rotate around an axis. It is often represented by the symbol "τ" and is measured in units of Newton-meters (N·m).

## 2. How is torque exerted by a flywheel calculated?

The torque exerted by a flywheel is calculated by multiplying the force applied to the flywheel by the distance from the center of the flywheel to the point of application of the force. This distance is known as the lever arm or moment arm.

## 3. What is the purpose of a flywheel?

A flywheel is a mechanical device that is used to store rotational energy. It is often used in machines that require a smooth and continuous supply of power, such as engines and turbines. The flywheel helps to maintain a constant speed and reduce fluctuations in rotational motion.

## 4. How does the size of a flywheel affect its torque?

The size of a flywheel does not directly affect its torque. However, a larger flywheel will have a greater moment of inertia, which means it will require more torque to accelerate or decelerate. This can result in a smoother and more stable rotation.

## 5. How does friction affect the torque exerted by a flywheel?

Friction can have a significant impact on the torque exerted by a flywheel. The presence of friction can decrease the efficiency of the flywheel and result in a lower torque output. This is why it is important for flywheels to be well-lubricated and properly maintained.

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