I= 1/2 mr^2 solve for mass m.
radius given
angular momentum: I*w=I*2
KE= 1/2 I w^2= 1/2 I *2^2
a uniform disk of moment of inertia 75kgm^2 and radius of gyration 3m rotates with an angular velocity of 2rad/s. determine d :
mass , radius , angular momentum . . and . . kinetic energy of d disk . . . .
3 answers
A uniform disc of moment of inertia 75kgm2 and radius of gyration 3m rotates with an angular velocity of 2rad/s. determine the (i) mass (ii) radius (iii) angular momentum and (iv) kinetic energy of the disc.
Given:
Moment of inertia, I = 75 kgm^2
Radius of gyration, k = 3 m
Angular velocity, ω = 2 rad/s
We can use the formula for moment of inertia in terms of mass and radius of the disk, I = (1/2) m R^2, where R is the radius of the disk.
(i) Solving for mass:
I = (1/2) m R^2
75 = (1/2) m R^2
m = 2I/R^2
(ii) Solving for radius:
We know that k = R/√(2), so:
3 = R/√(2)
R = 3√(2) m
(iii) Angular momentum:
Angular momentum, L = I ω
L = 75 × 2 = 150 kg m^2/s
(iv) Kinetic energy:
Kinetic energy, KE = (1/2) I ω^2
KE = (1/2) × 75 × 2^2
KE = 150 J
Moment of inertia, I = 75 kgm^2
Radius of gyration, k = 3 m
Angular velocity, ω = 2 rad/s
We can use the formula for moment of inertia in terms of mass and radius of the disk, I = (1/2) m R^2, where R is the radius of the disk.
(i) Solving for mass:
I = (1/2) m R^2
75 = (1/2) m R^2
m = 2I/R^2
(ii) Solving for radius:
We know that k = R/√(2), so:
3 = R/√(2)
R = 3√(2) m
(iii) Angular momentum:
Angular momentum, L = I ω
L = 75 × 2 = 150 kg m^2/s
(iv) Kinetic energy:
Kinetic energy, KE = (1/2) I ω^2
KE = (1/2) × 75 × 2^2
KE = 150 J
1 answer