# Why does my trimmer feels heavier when it is operating and its fully charged?

I have a Philips trimmer which when fully charged feels much heavier than when it is not charged. Also , the blades move much faster when it is fully charged I.e it’s weight , speed of blades kind of light increases as it more charged. What is it that can contribute to make it feel more heavy ?

Also , please let me know if you have any confusion in my Q or need more info.

• Could you clarify, "when its fully charged it feels heavier", you probably mean when you operate it? – NMech May 8 at 15:33
• @NMech Ofc. I use the trimmer that’s why. – Rider May 8 at 15:58
• Do you mean it is heavier when the battery is fully charged? Must be all the electrons... :) – Solar Mike May 8 at 16:25
• Do you mean you think it has more mass, or more moment of inertia? – Pete W May 8 at 18:08
• This seems to be your imagination playing tricks on you. Weigh it on a digital kitchen scales before and after. It will have the same mass. – Transistor May 8 at 18:25

## 1 Answer

When you are operating a trimmer you have a mass of about 10 gr moving side to side.

Let's assume that the amplitude of the motion is about 0.1mm, and that the frequency is f= 500Hz. So the blade will be vibrating:

$$x(t) = X\cdot \sin(2\pi f t)$$

That means that is velocity will be: $$\dot{x}(t) = (2\pi f)X\cdot \cos(2\pi f t)$$

and the acceleration will be:

$$\ddot{x}(t) = (2\pi f)^2X\cdot \sin(2\pi f t)$$

If you put the number in you get that the maximum acceleration is $$a= 986 \left[\frac{m}{s^2}\right]$$.

The RMS value would be $$a\approx 700\left[\frac{m}{s^2}\right]$$.

Therefore, the inertial force would be equal to:

$$F_{rms}= m\cdot a_{rms}= 7 [N]$$

That force would need to be counteracted by your hands (partly) and that is the force you perceive as the added weight of the trimmer.

Intentional Shortcuts in the analysis

The force calculated above would not actually be transmitted as it (I used approximate number to demonstrate the mechanism). The vibrating force of the blade is significantly attenuated by transmission through the (intentionally) heavy trimmer. If the trimmer were lighter at the same oscillating frequency, the force would be higher.

In real life, the frequencies are higher, and the forces. However, I intentionally did not use typical values, because I do not have damping ratios or stiffness matrix constants for the trimmer structure (which would actually be very much depended upon implementation).

Regarding the fully charged: I suspect your trimmer does not control the vibrating frequency actively. I am guessing it powers directly the (DC?) motor. That has the result, that the higher the frequency the higher the torque and the final velocity of the motor.

• Ok. I’ll check on it more too. 😊 Thanks – Rider May 8 at 18:10