A body of mass 8 kg moves in the xy-plane in a counterclockwise circular path of radius 3 meters centered at the origin, making one revolution every 10 seconds. At the time t=0, the body is at the rightmost point of the circle. A. Compute the centripetal force acting on the body at time t. ⟨, ⟩ B. Compute the magnitude of that force. HINT. Start with finding the angular velocity w [rad/s] of the body (the rate of change of its polar angle w.r.t. the center of rotation). Then find the position vector r→(t) of the body at time t. Then find its acceleration vector a→(t) at time t. Then use Newton's 2nd law to find the centripetal force F→(t).
A body of mass 8 kg moves in the xy-plane in a counterclockwise circular path of radius 3 meters centered at the origin, making one revolution every 10 seconds. At the time t=0, the body is at the rightmost point of the circle. A. Compute the centripetal force acting on the body at time t. ⟨, ⟩ B. Compute the magnitude of that force. HINT. Start with finding the angular velocity w [rad/s] of the body (the rate of change of its polar angle w.r.t. the center of rotation). Then find the position vector r→(t) of the body at time t. Then find its acceleration vector a→(t) at time t. Then use Newton's 2nd law to find the centripetal force F→(t).
A body of mass 8 kg moves in the xy-plane in a counterclockwise circular path of radius 3 meters centered at the origin, making one revolution every 10 seconds. At the time t=0, the body is at the rightmost point of the circle. A. Compute the centripetal force acting on the body at time t. ⟨, ⟩ B. Compute the magnitude of that force. HINT. Start with finding the angular velocity w [rad/s] of the body (the rate of change of its polar angle w.r.t. the center of rotation). Then find the position vector r→(t) of the body at time t. Then find its acceleration vector a→(t) at time t. Then use Newton's 2nd law to find the centripetal force F→(t).
A body of mass 8 kg moves in the xy-plane in a counterclockwise circular path of radius 3 meters centered at the origin, making one revolution every 10 seconds. At the time t=0, the body is at the rightmost point of the circle. A. Compute the centripetal force acting on the body at time t. ⟨, ⟩ B. Compute the magnitude of that force.
HINT. Start with finding the angular velocity w [rad/s] of the body (the rate of change of its polar angle w.r.t. the center of rotation). Then find the position vector r→(t) of the body at time t. Then find its acceleration vector a→(t) at time t. Then use Newton's 2nd law to find the centripetal force F→(t).
Definition Definition Force on a body along the radial direction. Centripetal force is responsible for the circular motion of a body. The magnitude of centripetal force is given by F C = m v 2 r m = mass of the body in the circular motion v = tangential velocity of the body r = radius of the circular path
Expert Solution
Step 1
Given,
First, let's find the angular velocity of the body. Since the body makes one revolution every 10 seconds, its angular velocity is:
Next, let's find the position vector r→(t) of the body at time t. Since the body starts at the rightmost point of the circle, its position vector at time t is:
r→(t) = (3 cos(ωt))i + (3 sin(ωt))j
where i and j are the unit vectors in the x- and y-directions, respectively.
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