![]() ![]() ![]() The power is then the amount of work done over a period of time. If a torque is applied on an object that rotates through an angle, then work is done by the torque. This equation is the rotational version of Newton's Second Law and applies to objects rotating about a fixed axis. ![]() , and the relationship between torque, angular acceleration, and moment of inertia is τ = I α The magnitude of the torque can be calculated by τ = F s t The moment arm is the perpendicular distance from the axis of rotation to the point of application of the force. A torque is the product of the force used to cause the rotation and the moment arm st. In exactly the same way, unbalanced torques & tau cause angular accelerations, and the moment of inertia I is the resistance to the torque. We learned back in Week 3 that unbalanced forces are the cause of accelerations and that mass is the resistance an object offers to the force. What is the magnitude of the centripetal force on the automobile? What is the cause of the centripetal force on the automobile?į c e n = m v 2 r = ( 1640 kg ) ( 15.0 m/s ) 2 ( 25.0 m ) = 14800 Nįigure 4 shows that torque increases when the length of the wrench increases. The equations above do not indicate the causes of the circular motion but merely give the relationship between the force and acceleration and the linear speed of the rotating object.Įxample: An automobile with a mass of 1,640 kg is driving around a curve with a radius of 25.0 m at a speed of 15.0 m/s. You are supplying the force needed to keep the ball moving in a circle. Notice that in order to keep the ball moving in a circle at a constant speed, you have to pull the string in toward the center of the circle. Go outdoors and carefully swing the ball in a circle over your head. Securely tie a small ball or other soft object to a length of string. The magnitude of the centripetal acceleration and the centripetal force can be calculated from these formulas. This unbalanced force is the cause of the circular motion and is called the centripetal force. If there is acceleration, then there must be an unbalanced force that points in the same direction as the acceleration. This acceleration is called the centripetal acceleration because it always points in toward the center of the circle. If the velocity is changing, there must be an acceleration causing the change. The velocity vectors are all the same length.Įven when an object is in uniform circular motion, the velocity is changing because the direction is constantly changing. Ω = ( 275 rev min ) ( 1 min 60 sec ) ( 2 π rad 1 rev ) = 28.8 rad/s v = ω r = ( 28.8 rad/s ) ( 0.250 m ) = 7.20 m/sįigure 3 shows the velocity is tangent to the circle. What is the angular velocity in radians per second and the linear speed of a point on the rim? In this equation, r is the radius of the circle, and T is the time required for the object to complete one revolution.Įxample: A wheel with radius 0.250 m is spinning at 275 rpm. The magnitude of the velocity tangent to the circle can be calculated by the following. If the object has a constant angular velocity, then the motion is called uniform circular motion. Δ E = E f i n a l − E i n i t i a l = W t o t a l If the force points in the opposite direction from the displacement, then the work is negative and the energy If the force points in the same direction as the displacement, then the work is positive and the energy of the system increases. ![]() If the force is perpendicular to the displacement, the work is 0. If there is no displacement, the work is 0. The units for the equation above are newton-metres, a unit which is the same as a joule. Figure 2 shows angular velocity and change in angle/change in time. ![]()
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