a) A 40 cm radius wheel is rotating at 20rad/sec. How fast is this wheel moving across the ground?
b) How far (in meters) will this wheel move in 6 seconds?
a) 20 rad/s * 40 cm/rad
b) [a)] * 6 s / 100 cm/m
a) To find the speed at which the wheel is moving across the ground, we need to calculate the linear velocity. The linear velocity can be calculated using the formula: linear velocity = radius * angular velocity.
Given:
Radius of the wheel (r) = 40 cm
Angular velocity (ω) = 20 rad/sec
Converting the radius to meters: 40 cm = 0.4 m
The linear velocity is:
Linear velocity = 0.4 m * 20 rad/sec = 8 m/s
Therefore, the wheel is moving across the ground at a speed of 8 m/s.
b) To find the distance the wheel will move in 6 seconds, we can use the formula: distance = linear velocity * time.
Given:
Linear velocity = 8 m/s
Time (t) = 6 seconds
The distance the wheel will move is:
Distance = 8 m/s * 6 seconds = 48 meters
Therefore, the wheel will move a distance of 48 meters in 6 seconds.
To determine how fast the wheel is moving across the ground (a) and how far it will move in a given time (b), we need to use the formula for linear velocity.
The linear velocity of a rotating object can be calculated by multiplying the angular velocity by the radius of the object.
a) To calculate the speed at which the wheel is moving across the ground, we can use the formula:
Linear velocity = Angular velocity × Radius.
Given that the radius of the wheel is 40 cm, which is equal to 0.4 meters, and the angular velocity is 20 rad/sec, we can plug these values into the formula:
Linear velocity = 20 rad/sec × 0.4 meters = 8 meters/sec.
Therefore, the wheel is moving across the ground at a speed of 8 meters per second.
b) To determine how far the wheel will move in 6 seconds, we can use the formula for distance:
Distance = Linear velocity × Time.
Using the calculated linear velocity of 8 meters/sec and the given time of 6 seconds, we can compute the distance:
Distance = 8 meters/sec × 6 seconds = 48 meters.
Therefore, the wheel will move a distance of 48 meters in 6 seconds.