A wheel of radius 30 cm is rotating at a rate of 2.0 revolutions every 0.080 s.
A. Through what angle, in radians, does the wheel rotate in 1.0 s?
B. What is the linear speed of a point on the wheel's rim?
C. What is the wheel's frequency of rotation?
Answer (3)
a) 2revs in 0.08s so in 1s thats 25revs therefore thats 50π radians in one second
b) well, ω=2π/T therefore ω=50π = 157.079rads^-1 and v=rω where r is in meters; v=0.3x157.079 v=47.123ms^-1
c) f=1/T f=1/period for one rotation 1 rotation = 0.08/2 = 0.04 f=1/0.04 f=25Hz
(a) The angle of the rotation of the wheel in 1.0 seconds is 157.1 radians.
(b) The linear speed of a point on the wheel's rim is 47.13 m/s.
(c) The wheel's frequency of rotation is 1500 rpm.
The given parameters;
radius of the wheel, r = 30 cm = 0.3 m
angular speed of the wheel, ω = 2 rev for 0.08 s
The angle of the rotation in 1.0 seconds is calculated as;
θ = ω t θ = ( 0.08 s 2 re v × 1 re v 2 π r a d ) × 1 θ = 157.1 r a d
The linear speed of the wheel is calculated as follows;
v = ω r v = ( 0.08 s 2 re v × 1 re v 2 π r a d ) × 0.3 v = 47.13 m / s
The wheel's frequency of rotation is calculated as follows;
N = 0.08 s 2 re v × 1 min 60 s N = 1500 RPM
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In 1.0 second, the wheel rotates approximately 157.08 radians. The linear speed of a point on the wheel's rim is around 47.12 m/s, and the wheel's frequency of rotation is 1500 rpm.
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