Respuesta :
Answer:
a) 23.04 rad/s
b) 0.79 m/s
c) 16 m/s²
d) 1.41 m
Explanation:
given,
radius of disk, r = 8.04 cm = 0.0804 m
Speed of disk, = 220 rpm
a) to get the angular speed in rad/s is quite easy since we already have it in rpm. All that is needed is conversion from rpm to rad/s
ω rad/s = 220 rpm * 2π rad/rev * 1/60 min/s
ω rad/s = 1382.48 / 60
ω rad/s = 23.04 rad/s
b) tangential speed at a point, 3.02 cm (0.0302 m) from the centre
Tangential speed is usually gotten from angular speed. Such that,
v = ωr
v = 23.04 * 0.0302
v = 0.70 m/s
c) radial acceleration of a point on the rim can also be expressed in terms of angular speed, such that.
a(r) = ω²r
a(r) = 23.04² * 0.0302
a(r) = 530.84 * 0.0302
a(r) = 16 m/s² directed towards the centre
d) total distance at a point on the rim.
The rim moves in 2.02 s, so,
d = ωrt
d = 23.04 * 0.0302 * 2.02
d = 1.41 m
Answer:
A) 128 rad/s
B) 3.87 m/s
C) 1317.17 m/s²
D) 20.79m
Explanation:
A) We are given the angular speed as 1220 rev/min. Now let's convert it to rad/s.
1220 (rev/min) x (2πrad/1rev) x (1min/60sec) = (1220 x 2π)/60 rad/s = 127.76 rad/s ≈ 128 rad/s
B) Formula for tangential speed is given as;
v = ωr
We know that ω = 128 rad/s
Also, r = 3.02cm = 0.0302m
Thus, v = 128 x 0.0302 = 3.87 m/s
C) Formula for radial acceleration is given as;
a_c = v²/r
From earlier, v = ωr
Thus, a_c = v²/r = (ωr)²/r = ω²r
On the rim, r = 8.04cm = 0.0804
a_c = 128² x 0.0804 = 1317.17 m/s²
D) We know that; distance/time = speed
Thus, distance = speed x time
D = vt
From earlier, v = ωr
Thus, D = ωrt
Plugging in the relevant values ;
D = 128 x 0.0804 x 2.02 = 20.79m
