a wheelof diameter 0.70 meterolls without slipping. a point at the top of the wheel moves with a tangential speed of 2.0 meter/second.
a) at what speed is the axis of the wheel moving?
b) What is the angular speed of the wheel?
The above answer is wrong, 1.b is actually 2.857 rad/s.W = v/r
W = 1/.35m
W = 2.86 rad/s
Circumference = pi*D = 3.14 * 0.7m = 2.20 m.
b. Va = 2m/s * 6.28rad/2.20m=5.71 rad/s = Angular velocity.
How can Va = 1m/s
The Tangential velocity is equal to its linear speed
Which is equal to the velocity of the center of mass.
V = 2Pi R/t = D/t
So
Va has to be = to 2m/s
I think the answer key is wrong
So
Va = 2m/s
and w= 5.7r/s
To answer these questions, we need to understand the relationship between linear and angular motion.
a) To determine the speed at which the axis of the wheel is moving, we need to consider the tangential velocity of the point at the top of the wheel.
The tangential velocity of a point on the wheel is given by the equation:
v = ω * r
where v is the tangential velocity, ω is the angular velocity (angular speed), and r is the radius of the wheel.
In this case, we are given the tangential velocity, v = 2.0 meters/second, and the radius, r = diameter/2 = 0.70/2 = 0.35 meters.
To find the angular velocity, ω, we rearrange the equation:
ω = v / r
Plugging in the given values:
ω = 2.0 / 0.35
Using a calculator or computer, we find:
ω ≈ 5.71 radians/second
The angular velocity represents how fast the wheel is rotating.
b) To find the angular speed of the wheel, we need to consider its circumference.
The circumference of a circle is given by:
C = 2πr
where C is the circumference and r is the radius.
In this case, the diameter of the wheel is given as 0.70 meters, so the radius is 0.35 meters.
The distance traveled by a point on the circumference of the wheel in one revolution (360 degrees or 2π radians) is equal to the circumference of the wheel.
Therefore, the linear speed of a point on the wheel's circumference is equal to its angular speed times the radius:
v = ω * r
We already know v = 2.0 meters/second and r = 0.35 meters. Rearranging the equation we get:
ω = v / r
Plugging in the given values:
ω = 2.0 / 0.35
Using a calculator or computer, we find:
ω ≈ 5.71 radians/second
So the angular speed of the wheel is approximately 5.71 radians/second.