Question

An electric trimmer blade has rotational inertia 1.55×10−4 kg*m^2.

What torque is needed to accelerate this blade from rest to 620 rpm in 1.35 s?

How much work was done to accelerate the blade?

Answer 1

i already found the torque which is 7.45*10^-4 but i dont know how to find the second part which asks how much work was done to accelerate the blade

Answer 2

F = ma

F = torque

accn = find angular accn

mass = inertia

Answer 3

Torque is 7.45*10^-4 N*m

Answer 4

angular acceleration = ??

Answer 5

it doesn't say.. the question only says "How much work was done to accelerate the blade?" so i don't know if they want the angular acceleration

Answer 6

you must find it first ... else you can't find the torque

Answer 7

620 rpm = angular velocity = 620*2*pi/60 = how much is that??

Answer 8

64.93

Answer 9

now angular acceleration = (620*2*pi/60-0)/1.35 /s^2, now use this in the relation

T = I*a
where T is torque, and a is angular accn and I is Inertia

Answer 10

Jeez .... you surprise me ... finding torque without angular accn

Answer 11

\[\omega=620*2\pi =64.93 rad/\sec\]

\[\alpha=\omega/t= 64.93/1.35= 48.09 rad/\sec^2\]
\[\tau=I*\alpha= 1.55*10^-4*48.09= 7.45*10^-3 N.m\]

this is how i found torque but i dont know how to find acceleration. what equation am i suppose to use?

Answer 12

alpha is your angular accn

Answer 13

that is exactly the equation you are supposed to use

Answer 14

ok thanks