During a tennis forehand, the angular velocity of the racquet is 20º/s just before impact with the ball. If the distance from the head of the racquet to the axis of rotation is 2m, what is the linear velocity of the head of the tennis racquet? Question 15Answera.40 m/s b.40º/s c.0.70º/s d.0.70 m/s e.Not possible to calculate
Question
During a tennis forehand, the angular velocity of the racquet is 20º/s just before impact with the ball. If the distance from the head of the racquet to the axis of rotation is 2m, what is the linear velocity of the head of the tennis racquet? Question 15Answera.40 m/s b.40º/s c.0.70º/s d.0.70 m/s e.Not possible to calculate
Solution
The linear velocity (v) of the head of the tennis racquet can be calculated using the formula:
v = rω
where: r = radius (distance from the axis of rotation to the point of interest) = 2m ω = angular velocity = 20º/s
However, the angular velocity needs to be converted from degrees per second to radians per second because the standard unit of angular velocity in this formula is radian per second.
1 radian = 57.3 degrees, so
ω = 20º/s ÷ 57.3 = 0.349 radians/s
Now, we can substitute r and ω into the formula:
v = 2m * 0.349 rad/s = 0.698 m/s
So, the linear velocity of the head of the tennis racquet is approximately 0.70 m/s. Therefore, the correct answer is d. 0.70 m/s.
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