is its magnitude ? Answer This is an example of uniform circular motion. Here R = cm. The angular speed ω is given by ω = π / T = π × / = .
rad/s The linear speed v is : v = ω R = . s - × cm = . cm s - The direction of velocity v is along the tangent to the circle at every point. The acceleration is directed towards the centre of the circle.
Since this direction changes continuously, acceleration here is not a constant vector. However, the magnitude of acceleration is constant: a = ω R = ( . s – ) ( cm) = . cm s - SUMMARY .
Scalar quantities are quantities with magnitudes only. Examples are distance, speed, mass and temperature. . Vector quantities are quantities with magnitude and direction both.
Examples are displacement, velocity and acceleration. They obey special rules of vector algebra. . A vector A multiplied by a real number λ is also a vector, whose magnitude is λ times the magnitude of the vector A and whose direction is the same or opposite depending upon whether λ is positive or negative.
. Two vectors A and B may be added graphically using head-to-tail method or parallelogram method . . Vector addition is commutative : A + B = B + A It also obeys the associative law : ( A + B ) + C = A + ( B + C ) .
A null or zero vector is a vector with zero magnitude. Since the magnitude is zero, we don’t have to specify its direction. It has the properties : A + = A λ = A = . The subtraction of vector B from A is defined as the sum of A and – B : A – B = A + ( – B ) .
A vector A can be resolved into component along two given vectors a and b lying in the same plane : A